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  Subjects -> MATHEMATICS (Total: 955 journals)
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    - MATHEMATICS (706 journals)
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MATHEMATICS (706 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 4)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 3)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 7)
ACM Transactions on Algorithms (TALG)     Hybrid Journal   (Followers: 15)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 3)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 27)
Acta Applicandae Mathematicae     Hybrid Journal   (Followers: 1)
Acta Mathematica     Hybrid Journal   (Followers: 11)
Acta Mathematica Hungarica     Hybrid Journal   (Followers: 2)
Acta Mathematica Scientia     Full-text available via subscription   (Followers: 5)
Acta Mathematica Sinica, English Series     Hybrid Journal   (Followers: 6)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 9)
Advances in Applied Clifford Algebras     Hybrid Journal   (Followers: 3)
Advances in Calculus of Variations     Hybrid Journal   (Followers: 2)
Advances in Catalysis     Full-text available via subscription   (Followers: 5)
Advances in Complex Systems     Hybrid Journal   (Followers: 6)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 18)
Advances in Decision Sciences     Open Access   (Followers: 3)
Advances in Difference Equations     Open Access   (Followers: 3)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 13)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 2)
Advances in Materials Sciences     Open Access   (Followers: 14)
Advances in Mathematical Physics     Open Access   (Followers: 3)
Advances in Mathematics     Full-text available via subscription   (Followers: 10)
Advances in Numerical Analysis     Open Access   (Followers: 4)
Advances in Operations Research     Open Access   (Followers: 12)
Advances in Porous Media     Full-text available via subscription   (Followers: 5)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 5)
Advances in Science and Research (ASR)     Open Access   (Followers: 4)
Aequationes Mathematicae     Hybrid Journal   (Followers: 2)
African Journal of Educational Studies in Mathematics and Sciences     Full-text available via subscription   (Followers: 5)
African Journal of Mathematics and Computer Science Research     Open Access   (Followers: 4)
Afrika Matematika     Hybrid Journal   (Followers: 1)
Air, Soil & Water Research     Open Access   (Followers: 11)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Algebra and Logic     Hybrid Journal   (Followers: 5)
Algebra Colloquium     Hybrid Journal   (Followers: 4)
Algebra Universalis     Hybrid Journal   (Followers: 2)
Algorithmic Operations Research     Full-text available via subscription   (Followers: 5)
Algorithms     Open Access   (Followers: 11)
Algorithms Research     Open Access   (Followers: 1)
American Journal of Computational and Applied Mathematics     Open Access   (Followers: 5)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 6)
American Journal of Operations Research     Open Access   (Followers: 5)
American Mathematical Monthly     Full-text available via subscription   (Followers: 6)
An International Journal of Optimization and Control: Theories & Applications     Open Access   (Followers: 8)
Analele Universitatii Ovidius Constanta - Seria Matematica     Open Access   (Followers: 1)
Analysis     Hybrid Journal   (Followers: 2)
Analysis and Applications     Hybrid Journal   (Followers: 1)
Analysis and Mathematical Physics     Hybrid Journal   (Followers: 4)
Analysis Mathematica     Full-text available via subscription  
Annales Mathematicae Silesianae     Open Access  
Annales mathématiques du Québec     Hybrid Journal   (Followers: 4)
Annales UMCS, Mathematica     Open Access   (Followers: 1)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica     Open Access  
Annali di Matematica Pura ed Applicata     Hybrid Journal   (Followers: 1)
Annals of Combinatorics     Hybrid Journal   (Followers: 3)
Annals of Data Science     Hybrid Journal   (Followers: 11)
Annals of Discrete Mathematics     Full-text available via subscription   (Followers: 6)
Annals of Mathematics     Full-text available via subscription  
Annals of Mathematics and Artificial Intelligence     Hybrid Journal   (Followers: 12)
Annals of Pure and Applied Logic     Open Access   (Followers: 2)
Annals of the Alexandru Ioan Cuza University - Mathematics     Open Access  
Annals of the Institute of Statistical Mathematics     Hybrid Journal   (Followers: 1)
Annals of West University of Timisoara - Mathematics     Open Access  
Annuaire du Collège de France     Open Access   (Followers: 5)
ANZIAM Journal     Open Access   (Followers: 1)
Applicable Algebra in Engineering, Communication and Computing     Hybrid Journal   (Followers: 2)
Applications of Mathematics     Hybrid Journal   (Followers: 1)
Applied Categorical Structures     Hybrid Journal   (Followers: 2)
Applied Computational Intelligence and Soft Computing     Open Access   (Followers: 11)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 6)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 6)
Applied Mathematics - A Journal of Chinese Universities     Hybrid Journal  
Applied Mathematics Letters     Full-text available via subscription   (Followers: 1)
Applied Mathematics Research eXpress     Hybrid Journal   (Followers: 1)
Applied Network Science     Open Access   (Followers: 3)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 2)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 5)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Armenian Journal of Mathematics     Open Access  
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 20)
Asia-Pacific Journal of Operational Research     Hybrid Journal   (Followers: 3)
Asian Journal of Algebra     Open Access   (Followers: 1)
Asian Journal of Current Engineering & Maths     Open Access  
Asian-European Journal of Mathematics     Hybrid Journal   (Followers: 2)
Australian Mathematics Teacher, The     Full-text available via subscription   (Followers: 6)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 4)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access   (Followers: 1)
Baltic International Yearbook of Cognition, Logic and Communication     Open Access   (Followers: 1)
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access   (Followers: 2)
BIT Numerical Mathematics     Hybrid Journal  
BoEM - Boletim online de Educação Matemática     Open Access  
Boletim Cearense de Educação e História da Matemática     Open Access  
Boletim de Educação Matemática     Open Access  
Boletín de la Sociedad Matemática Mexicana     Hybrid Journal  
Bollettino dell'Unione Matematica Italiana     Full-text available via subscription   (Followers: 1)
British Journal of Mathematical and Statistical Psychology     Full-text available via subscription   (Followers: 21)
Bruno Pini Mathematical Analysis Seminar     Open Access  
Buletinul Academiei de Stiinte a Republicii Moldova. Matematica     Open Access   (Followers: 11)
Bulletin des Sciences Mathamatiques     Full-text available via subscription   (Followers: 4)
Bulletin of Dnipropetrovsk University. Series : Communications in Mathematical Modeling and Differential Equations Theory     Open Access   (Followers: 1)
Bulletin of Mathematical Sciences     Open Access   (Followers: 1)
Bulletin of Symbolic Logic     Full-text available via subscription   (Followers: 2)
Bulletin of the Australian Mathematical Society     Full-text available via subscription   (Followers: 1)
Bulletin of the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 4)
Bulletin of the Malaysian Mathematical Sciences Society     Hybrid Journal  
Calculus of Variations and Partial Differential Equations     Hybrid Journal  
Canadian Journal of Science, Mathematics and Technology Education     Hybrid Journal   (Followers: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 2)
CHANCE     Hybrid Journal   (Followers: 5)
Chaos, Solitons & Fractals     Hybrid Journal   (Followers: 3)
ChemSusChem     Hybrid Journal   (Followers: 7)
Chinese Annals of Mathematics, Series B     Hybrid Journal  
Chinese Journal of Catalysis     Full-text available via subscription   (Followers: 2)
Chinese Journal of Mathematics     Open Access  
Clean Air Journal     Full-text available via subscription   (Followers: 1)
Cogent Mathematics     Open Access   (Followers: 2)
Cognitive Computation     Hybrid Journal   (Followers: 4)
Collectanea Mathematica     Hybrid Journal  
College Mathematics Journal     Full-text available via subscription   (Followers: 4)
COMBINATORICA     Hybrid Journal  
Combinatorics, Probability and Computing     Hybrid Journal   (Followers: 4)
Combustion Theory and Modelling     Hybrid Journal   (Followers: 14)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
Communications in Combinatorics and Optimization     Open Access  
Communications in Contemporary Mathematics     Hybrid Journal  
Communications in Mathematical Physics     Hybrid Journal   (Followers: 2)
Communications On Pure & Applied Mathematics     Hybrid Journal   (Followers: 3)
Complex Analysis and its Synergies     Open Access   (Followers: 2)
Complex Variables and Elliptic Equations: An International Journal     Hybrid Journal  
Complexus     Full-text available via subscription  
Composite Materials Series     Full-text available via subscription   (Followers: 8)
Compositio Mathematica     Full-text available via subscription   (Followers: 1)
Comptes Rendus Mathematique     Full-text available via subscription   (Followers: 1)
Computational and Applied Mathematics     Hybrid Journal   (Followers: 2)
Computational and Mathematical Methods in Medicine     Open Access   (Followers: 2)
Computational and Mathematical Organization Theory     Hybrid Journal   (Followers: 2)
Computational Complexity     Hybrid Journal   (Followers: 4)
Computational Mathematics and Modeling     Hybrid Journal   (Followers: 8)
Computational Mechanics     Hybrid Journal   (Followers: 5)
Computational Methods and Function Theory     Hybrid Journal  
Computational Optimization and Applications     Hybrid Journal   (Followers: 7)
Computers & Mathematics with Applications     Full-text available via subscription   (Followers: 8)
Concrete Operators     Open Access   (Followers: 5)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 12)
Cuadernos de Investigación y Formación en Educación Matemática     Open Access  
Cubo. A Mathematical Journal     Open Access  
Current Research in Biostatistics     Open Access   (Followers: 9)
Czechoslovak Mathematical Journal     Hybrid Journal   (Followers: 1)
Demographic Research     Open Access   (Followers: 10)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 29)
Developments in Clay Science     Full-text available via subscription   (Followers: 1)
Developments in Mineral Processing     Full-text available via subscription   (Followers: 3)
Dhaka University Journal of Science     Open Access  
Differential Equations and Dynamical Systems     Hybrid Journal   (Followers: 3)
Differentsial'nye Uravneniya     Open Access  
Discrete Mathematics     Hybrid Journal   (Followers: 8)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae - General Algebra and Applications     Open Access  
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Diskretnaya Matematika     Full-text available via subscription  
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Akademii Nauk     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Eco Matemático     Open Access  
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
Electronic Journal of Differential Equations     Open Access  
Electronic Journal of Graph Theory and Applications     Open Access   (Followers: 2)
Electronic Notes in Discrete Mathematics     Full-text available via subscription   (Followers: 2)
Elemente der Mathematik     Full-text available via subscription   (Followers: 4)

        1 2 3 4 | Last

Journal Cover Computers & Mathematics with Applications
  [SJR: 1.092]   [H-I: 84]   [8 followers]  Follow
    
   Full-text available via subscription Subscription journal
   ISSN (Print) 0898-1221
   Published by Elsevier Homepage  [3175 journals]
  • A hierarchical computational model for moving thermal loads and phase
           changes with applications to selective laser melting
    • Authors: S. Kollmannsberger; A. Özcan; M. Carraturo; N. Zander; E. Rank
      Pages: 1483 - 1497
      Abstract: Publication date: 1 March 2018
      Source:Computers & Mathematics with Applications, Volume 75, Issue 5
      Author(s): S. Kollmannsberger, A. Özcan, M. Carraturo, N. Zander, E. Rank
      Computational heat transfer analysis often involves moving fluxes which induce traveling fronts of phase change coupled to one or more field variables. Examples are the transient simulation of melting, welding or of additive manufacturing processes, where material changes its state and the controlling fields are temperature and structural deformation. One of the challenges for a numerical computation of these processes is their multi-scale nature with a highly localized zone of phase transition which may travel over a large domain of a body. Here, a transient local adaptation of the approximation, with not only a refinement at the phase front, but also a de-refinement in regions, where the front has passed is of advantage because the de-refinement can assure a bounded number of degrees of freedom which is independent from the traveling length of the front. We present a computational model of this process which involves three novelties: (a) a very low number of degrees of freedom which yet yields a comparatively high accuracy. The number of degrees of freedom is, additionally, kept practically constant throughout the duration of the simulation. This is achieved by means of the multi-level h p -finite element method. Its exponential convergence is verified for the first time against a semi-analytic, three-dimensional transient linear thermal benchmark with a traveling source term which models a laser beam. ( b) A hierarchical treatment of the state variables. To this end, the state of the material is managed on a separate, octree-like grid. This material grid may refine or coarsen independently of the discretization used for the temperature field. This methodology is verified against an analytic benchmark of a melting bar computed in three dimensions in which phase changes of the material occur on a rapidly advancing front. (c) The combination of these technologies to demonstrate its potential for the computational modeling of selective laser melting processes. To this end, the computational methodology is extended by the finite cell method which allows for accurate simulations in an embedded domain setting. This opens the new modeling possibility that neither a scan vector nor a layer of material needs to conform to the discretization of the finite element mesh but can form only a fraction within the discretization of the field- and state variables.

      PubDate: 2018-02-26T06:08:30Z
      DOI: 10.1016/j.camwa.2017.11.014
       
  • An example of explicit implementation strategy and preconditioning for the
           high order edge finite elements applied to the time-harmonic Maxwell’s
           equations
    • Authors: Marcella Bonazzoli; Victorita Dolean; Frédéric Hecht; Francesca Rapetti
      Pages: 1498 - 1514
      Abstract: Publication date: 1 March 2018
      Source:Computers & Mathematics with Applications, Volume 75, Issue 5
      Author(s): Marcella Bonazzoli, Victorita Dolean, Frédéric Hecht, Francesca Rapetti
      In this paper we focus on high order finite element approximations of the electric field combined with suitable preconditioners, to solve the time-harmonic Maxwell’s equations in waveguide configurations. The implementation of high order curl-conforming finite elements is quite delicate, especially in the three-dimensional case. Here, we explicitly describe an implementation strategy, which has been embedded in the open source finite element software FreeFem++ (http://www.freefem.org/ff++/). In particular, we use the inverse of a generalized Vandermonde matrix to build basis functions in duality with the degrees of freedom, resulting in an easy-to-use but powerful interpolation operator. We carefully address the problem of applying the same Vandermonde matrix to possibly differently oriented tetrahedra of the mesh over the computational domain. We investigate the preconditioning for Maxwell’s equations in the time-harmonic regime, which is an underdeveloped issue in the literature, particularly for high order discretizations. In the numerical experiments, we study the effect of varying several parameters on the spectrum of the matrix preconditioned with overlapping Schwarz methods, both for 2d and 3d waveguide configurations.

      PubDate: 2018-02-26T06:08:30Z
      DOI: 10.1016/j.camwa.2017.11.013
       
  • L1 Fourier spectral methods for a class of generalized two-dimensional
           time fractional nonlinear anomalous diffusion equations
    • Authors: Rumeng Zheng; Xiaoyun Jiang; Hui Zhang
      Pages: 1515 - 1530
      Abstract: Publication date: 1 March 2018
      Source:Computers & Mathematics with Applications, Volume 75, Issue 5
      Author(s): Rumeng Zheng, Xiaoyun Jiang, Hui Zhang
      In this paper, L1 Fourier spectral methods are derived to obtain the numerical solutions for a class of generalized two-dimensional time-fractional nonlinear anomalous diffusion equations involving Caputo fractional derivative. Firstly, we establish the L1 Fourier Galerkin full discrete and L1 Fourier collocation schemes with Fourier spectral discretization in spatial direction and L1 difference method in temporal direction. Secondly, stability and convergence for both Galerkin and collocation approximations are proved. It is shown that the proposed methods are convergent with spectral accuracy in space and ( 2 − α ) order accuracy in time. For implementation, the equivalence between pseudospectral method and collocation method is discussed. Furthermore, a numerical algorithm of Fourier pseudospectral method is developed based on two-dimensional fast Fourier transform (FFT2) technique. Finally, numerical examples are provided to test the theoretical claims. As is shown in the numerical experiments, Fourier spectral methods are powerful enough with excellent efficiency and accuracy.

      PubDate: 2018-02-26T06:08:30Z
      DOI: 10.1016/j.camwa.2017.11.017
       
  • Modeling the quantum tunneling effect for a particle with intrinsic
           
    • Authors: Alexander V. Chichurin; Elena M. Ovsiyuk; Viktor M. Red’kov
      Pages: 1550 - 1565
      Abstract: Publication date: 1 March 2018
      Source:Computers & Mathematics with Applications, Volume 75, Issue 5
      Author(s): Alexander V. Chichurin, Elena M. Ovsiyuk, Viktor M. Red’kov
      Generalized Schrödinger equation for Cox spin zero particle is studied in presence of magnetic field on the background of Lobachevsky space. Separation of the variables is performed. An equation describing motion along the axis z turns out to be much more complicated than when describing the Cox particle in Minkowski space. The form of the effective potential curve indicates that we have a quantum-mechanical problem of the tunneling type. The derived equation has 6 regular singular points. To physical domains z = ± ∞ there correspond the singular points 0 and 1 of the derived equation. Frobenius solutions of the equation are constructed, convergence of the relevant series is examined by Poincaré–Perron method. These series are convergent in the whole physical domain z ∈ ( − ∞ , + ∞ ) . Visualization of constructed solutions and numerical study of the tunneling effect are performed.

      PubDate: 2018-02-26T06:08:30Z
      DOI: 10.1016/j.camwa.2017.11.019
       
  • Asymmetric thermal buckling of temperature dependent annular FGM plates on
           a partial elastic foundation
    • Authors: H. Bagheri; Y. Kiani; M.R. Eslami
      Pages: 1566 - 1581
      Abstract: Publication date: 1 March 2018
      Source:Computers & Mathematics with Applications, Volume 75, Issue 5
      Author(s): H. Bagheri, Y. Kiani, M.R. Eslami
      In this investigation, the asymmetrical buckling behaviour of FGM annular plates resting on partial Winkler-type elastic foundation under uniform temperature elevation is investigated. Material properties of the plate are assumed to be temperature dependent. Each property of the plate is graded across the thickness direction using a power law function. First order shear deformation plate theory and von Kármán type of geometrical nonlinearity are used to obtain the equilibrium equations and the associated boundary conditions. Prebuckling deformations and stresses of the plate are obtained considering the deflection-less conditions. Only plates which are clamped on both inner and outer edges are considered. Applying the adjacent equilibrium criterion, the linearised stability equations are obtained. The governing equations are divided into two sets. The first set, which is associated with the in-contact region and the second set which is related to contact-less region. The resulting equations are solved using a hybrid method, including the analytical trigonometric functions through the circumferential direction and generalised differential quadratures method through the radial direction. The resulting system of eigenvalue problem is solved iteratively to obtain the critical conditions of the plate, the associated circumferential mode number and buckled shape of the plate. Benchmark results are given in tabular and graphical presentations dealing with critical buckling temperature and buckled shape of the plate. Numerical results are given to explore the effects of elastic foundation, foundation radius, plate thickness, plate hole size, and power law index of the graded plate. It is shown that, stiffness foundation, and radius of foundation may change the buckled shape of the plate in both circumferential and radial directions. Furthermore, as the stiffness of the foundation or radius of foundation increases, critical buckling temperature of the plate enhances.

      PubDate: 2018-02-26T06:08:30Z
      DOI: 10.1016/j.camwa.2017.11.021
       
  • C1 continuous h-adaptive least-squares spectral element method for
           phase-field models
    • Authors: Keunsoo Park; Marc Gerritsma; Maria Fernandino
      Pages: 1582 - 1594
      Abstract: Publication date: 1 March 2018
      Source:Computers & Mathematics with Applications, Volume 75, Issue 5
      Author(s): Keunsoo Park, Marc Gerritsma, Maria Fernandino
      To describe the interfacial dynamics between two phases using the phase-field method, the interfacial region needs to be close enough to a sharp interface so as to reproduce the correct physics. Due to the high gradients of the solution within the interfacial region and consequent high computational cost, the use of the phase-field method has been limited to the small-scale problems whose characteristic length is similar to the interfacial thickness. By using finer mesh at the interface and coarser mesh in the rest of computational domain, the phase-field methods can handle larger scale of problems with realistic interface thicknesses. In this work, a C 1 continuous h -adaptive mesh refinement technique with the least-squares spectral element method is presented. It is applied to the Navier–Stokes-Cahn–Hilliard (NSCH) system and the isothermal Navier–Stokes–Korteweg (NSK) system. Hermite polynomials are used to give global differentiability in the approximated solution, and a space–time coupled formulation and the element-by-element technique are implemented. Two refinement strategies based on the solution gradient and the local error estimators are suggested, and they are compared in two numerical examples.

      PubDate: 2018-02-26T06:08:30Z
      DOI: 10.1016/j.camwa.2017.11.026
       
  • Fractal dimensions of random attractors for stochastic
           Benjamin–Bona–Mahony equation on unbounded domains
    • Authors: Fuqi Yin; Xueli Li
      Pages: 1595 - 1615
      Abstract: Publication date: 1 March 2018
      Source:Computers & Mathematics with Applications, Volume 75, Issue 5
      Author(s): Fuqi Yin, Xueli Li
      This paper considers random attractor and its fractal dimension for Benjamin–Bona–Mahony equation driven by additive white noise on unbounded domains . Firstly, we investigate the existence of random attractor for the random dynamical system defined on an unbounded domain. Secondly, we present criterion for estimating an upper bound of the fractal dimension of a random invariant set of a random dynamical system on a separable Banach space. Finally, we apply expectations of some random variables and these conditions to prove the finiteness of fractal dimension of the random attractors for stochastic Benjamin–Bona–Mahony equation driven by additive white noise.

      PubDate: 2018-02-26T06:08:30Z
      DOI: 10.1016/j.camwa.2017.11.025
       
  • A modified Black–Scholes pricing formula for European options with
           bounded underlying prices
    • Authors: Song-Ping Zhu; Xin-Jiang He
      Pages: 1635 - 1647
      Abstract: Publication date: 1 March 2018
      Source:Computers & Mathematics with Applications, Volume 75, Issue 5
      Author(s): Song-Ping Zhu, Xin-Jiang He
      In this paper, a modified Black–Scholes (B–S) model is proposed, based on a revised assumption that the range of the underlying price varies within a finite zone, rather than being allowed to vary in a semi-infinite zone as presented in the classical B–S theory. This is motivated by the fact that the underlying price of any option can never reach infinity in reality; a trader may use our new formula to adjust the option price that he/she is willing to long or short. To develop this modified option pricing formula, we assume that a trader has a view on the realistic price range of a particular asset and the log-returns follow a truncated normal distribution within this price range. After a closed-form pricing formula for European call options has been successfully derived, some numerical experiments are conducted. To further demonstrate the meaning of the proposed model, empirical studies are carried out to compare the pricing performance of our model and that of the B–S model with real market data.

      PubDate: 2018-02-26T06:08:30Z
      DOI: 10.1016/j.camwa.2017.11.023
       
  • Rigorous cubical approximation and persistent homology of continuous
           functions
    • Authors: Paweł Dłotko; Thomas Wanner
      Pages: 1648 - 1666
      Abstract: Publication date: 1 March 2018
      Source:Computers & Mathematics with Applications, Volume 75, Issue 5
      Author(s): Paweł Dłotko, Thomas Wanner
      The interaction between discrete and continuous mathematics lies at the heart of many fundamental problems in applied mathematics and computational sciences. In this paper we discuss the problem of discretizing vector-valued functions defined on finite-dimensional Euclidean spaces in such a way that the discretization error is bounded by a pre-specified small constant. While the approximation scheme has a number of potential applications, we consider its usefulness in the context of computational homology. More precisely, we demonstrate that our approximation procedure can be used to rigorously compute the persistent homology of the original continuous function on a compact domain, up to small explicitly known and verified errors. In contrast to other work in this area, our approach requires minimal smoothness assumptions on the underlying function.

      PubDate: 2018-02-26T06:08:30Z
      DOI: 10.1016/j.camwa.2017.11.027
       
  • Jacobi elliptic wave solutions for two variable coefficients cylindrical
           Korteweg–de Vries models arising in dusty plasmas by using direct
           reduction method
    • Authors: Rehab M. El-Shiekh
      Pages: 1676 - 1684
      Abstract: Publication date: Available online 11 January 2018
      Source:Computers & Mathematics with Applications
      Author(s): Rehab M. El-Shiekh
      In this paper, generalized models for both ( 2 + 1 )-dimensional cylindrical modified Korteweg–de Vries (cmKdV) equation with variable coefficients and ( 3 + 1 )-dimensional variable coefficients cylindrical Korteweg–de Vries (cKdV) equation are studied by direct reduction method. A direct reduction to nonlinear ordinary differential equations in the form of Riccati equations obtained for the considered equations under some integrability conditions. The search for solutions for the reduced Riccati equations has yielded many Jacobi elliptic wave solutions, solitary and periodic wave solutions for both ( 2 + 1 )-dimensional cmKdV and ( 3 + 1 )-dimensional cKdV equations. Physical application for the obtained solutions as dust ion acoustic waves in plasma physics is given

      PubDate: 2018-02-05T05:41:11Z
      DOI: 10.1016/j.camwa.2017.11.031
       
  • Localized radial basis functions-based pseudo-spectral method (LRBF-PSM)
           for nonlocal diffusion problems
    • Authors: Wei Zhao; Yiu-chung Hon; Martin Stoll
      Pages: 1685 - 1704
      Abstract: Publication date: 1 March 2018
      Source:Computers & Mathematics with Applications, Volume 75, Issue 5
      Author(s): Wei Zhao, Yiu-chung Hon, Martin Stoll
      Spectral/pseudo-spectral methods based on high order polynomials have been successfully used for solving partial differential and integral equations. In this paper, we will present the use of a localized radial basis functions-based pseudo-spectral method (LRBF-PSM) for solving 2D nonlocal problems with radial nonlocal kernels. The basic idea of the LRBF-PSM is to construct a set of orthogonal functions by RBFs on each overlapping sub-domain from which the global solution can be obtained by extending the approximation on each sub-domain to the entire domain. Numerical implementation indicates that the proposed LRBF-PSM is simple to use, efficient and robust to solve various nonlocal problems.

      PubDate: 2018-02-26T06:08:30Z
      DOI: 10.1016/j.camwa.2017.11.030
       
  • A separation of the boundary geometry from the boundary functions in PIES
           for 3D problems modeled by the Navier–Lamé equation
    • Authors: Eugeniusz Zieniuk; Krzysztof Szerszeń
      Pages: 1067 - 1094
      Abstract: Publication date: Available online 1 February 2018
      Source:Computers & Mathematics with Applications
      Author(s): Eugeniusz Zieniuk, Krzysztof Szerszeń
      In this paper, we present a modification of the Somigliana identity for the 3D Navier–Lamé equation in order to analytically include in its mathematical formalism the boundary represented by Coons and Bézier parametric surface patches. As a result, the equations called the parametric integral equation system (PIES) with integrated boundary shape are obtained. The PIES formulation is independent from the boundary shape representation and it is always, for any shape, defined in the parametric domain and not on the physical boundary as in the traditional boundary integral equations (BIE). This feature is also helpful during numerical solving of PIES, as from a formal point of view, a separation between the approximation of the boundary and the boundary functions is obtained. In this paper, the generalized Chebyshev series are used to approximate the boundary functions. Numerical examples demonstrate the effectiveness of the presented strategy for boundary representation and indicate the high accuracy of the obtained results.

      PubDate: 2018-02-05T05:41:11Z
      DOI: 10.1016/j.camwa.2017.10.036
       
  • Preconditioned HSS iteration method and its non-alternating variant for
           continuous Sylvester equations
    • Authors: Xu Li; Hai-Feng Huo; Ai-Li Yang
      Pages: 1095 - 1106
      Abstract: Publication date: 15 February 2018
      Source:Computers & Mathematics with Applications, Volume 75, Issue 4
      Author(s): Xu Li, Hai-Feng Huo, Ai-Li Yang
      Bai (2010) proposed an efficient Hermitian and skew-Hermitian splitting (HSS) iteration method for solving a broad class of large sparse continuous Sylvester equations. To further improve the efficiency of the HSS method, in this paper we present a preconditioned HSS (PHSS) iteration method and its non-alternating variant (NPHSS) for this matrix equation. The convergence properties of the PHSS and NPHSS methods are studied in depth and the quasi-optimal values of the iteration parameters for the two methods are also derived. Moreover, to reduce the computational cost, we establish the inexact variants of the two iteration methods. Numerical experiments illustrate the efficiency and robustness of the two iteration methods and their inexact variants.

      PubDate: 2018-02-26T06:08:30Z
      DOI: 10.1016/j.camwa.2017.10.028
       
  • A study on the 3D position estimation of ventricular borders extracted
           from 2D echocardiography data
    • Authors: Chi Young Ahn; Sangwoon Yun
      Pages: 1143 - 1158
      Abstract: Publication date: 15 February 2018
      Source:Computers & Mathematics with Applications, Volume 75, Issue 4
      Author(s): Chi Young Ahn, Sangwoon Yun
      We study on the reconstruction of 3D left ventricle(LV) using only 2D echocardiography data and information on apical long-axis views. Especially, this paper focuses on determining the 3D position of LV contours extracted from 2D echocardiography images. First we mathematically model the relationship between LV contours on the apical views and their corresponding 3D positions. The relationship is expressed as a linear equation in which the right-hand side is the measured data consisting of all the LV contour points on each view and the coefficient matrix is an unknown matrix that transforms the unknown 3D positions into contour points on their related apical view, with distance and orthogonality conditions on the coefficient matrix and the 3D positions. Next we consider a non-convex constrained minimization problem to determine the coefficient matrix and the 3D positions. To solve this minimization problem, we adopt two block coordinate descent method with a solver in OPTI for quadratically constrained quadratic program. For validating the proposed method, some numerical experiments are performed with synthetic data. The experimental results show that the proposed model is promising and available for real echocardiographydata.

      PubDate: 2018-02-26T06:08:30Z
      DOI: 10.1016/j.camwa.2017.10.025
       
  • Discrete kinetic theory for 2D modeling of a moving crowd: Application to
           the evacuation of a non-connected bounded domain
    • Authors: A. Elmoussaoui; P. Argoul; M. El Rhabi; A. Hakim
      Pages: 1159 - 1180
      Abstract: Publication date: 15 February 2018
      Source:Computers & Mathematics with Applications, Volume 75, Issue 4
      Author(s): A. Elmoussaoui, P. Argoul, M. El Rhabi, A. Hakim
      This paper concerns the mathematical modeling of the motion of a crowd in a non connected bounded domain, based on kinetic and stochastic game theories. The proposed model is a mesoscopic probabilistic approach that retains features obtained from both micro- and macro-scale representations; pedestrian interactions with various obstacles being managed from a probabilistic perspective. A proof of the existence and uniqueness of the proposed mathematical model’s solution is given for large times. A numerical resolution scheme based on the splitting method is implemented and then applied to crowd evacuation in a non connected bounded domain with one rectangular obstacle. The evacuation time of the room is then calculated by our technique, according to the dimensions and position of a square-shaped obstacle, and finally compared to the time obtained by a deterministic approach by means of randomly varying some of its parameters.

      PubDate: 2018-02-26T06:08:30Z
      DOI: 10.1016/j.camwa.2017.10.023
       
  • Superconvergence in a DPG method for an ultra-weak formulation
    • Authors: Thomas
      Abstract: Publication date: 1 March 2018
      Source:Computers & Mathematics with Applications, Volume 75, Issue 5
      Author(s): Thomas Führer
      In this work we study a DPG method for an ultra-weak variational formulation of a reaction–diffusion problem. We improve existing a priori convergence results by sharpening an approximation result for the numerical flux. By duality arguments we show that higher convergence rates for the scalar field variable are obtained if the polynomial order of the corresponding approximation space is increased by one. Furthermore, we introduce a simple elementwise postprocessing of the solution and prove superconvergence. Numerical experiments indicate that the obtained results are valid beyond the underlying model problem.

      PubDate: 2018-02-26T06:08:30Z
       
  • Depth-averaged Lattice Boltzmann and Finite Element methods for
           single-phase flows in fractures with obstacles
    • Authors: Michal Dzikowski; Lukasz Jasinski; Marcin Dabrowski
      Abstract: Publication date: Available online 24 February 2018
      Source:Computers & Mathematics with Applications
      Author(s): Michal Dzikowski, Lukasz Jasinski, Marcin Dabrowski
      We use Lattice Boltzmann Method (LBM) MRT and Cumulant schemes to study the performance and accuracy of single-phase flow modeling for propped fractures. The simulations are run using both the two- and three-dimensional Stokes equations, and a 2.5D Stokes–Brinkman approximate model. The LBM results are validated against Finite Element Method (FEM) simulations and an analytical solution to the Stokes–Brinkman flow around an isolated circular obstacle. Both LBM and FEM 2.5D Stokes–Brinkman models are able to reproduce the analytical solution for an isolated circular obstacle. In the case of 2D Stokes and 2.5D Stokes–Brinkman models, the differences between the extrapolated fracture permeabilities obtained with LBM and FEM simulations for fractures with multiple obstacles are below 1%. The differences between the fracture permeabilities computed using 3D Stokes LBM and FEM simulations are below 8% . The differences between the 3D Stokes and 2.5 Stokes–Brinkman results are less than 7% for FEM study, and 8% for the LBM case. The velocity perturbations that are introduced around the obstacles are not fully captured by the parabolic velocity profile inherent to the 2.5D Stokes–Brinkman model.

      PubDate: 2018-02-26T06:08:30Z
      DOI: 10.1016/j.camwa.2018.02.010
       
  • Exploring high-order three dimensional virtual elements: Bases and
           stabilizations
    • Authors: F. Dassi; L. Mascotto
      Abstract: Publication date: Available online 24 February 2018
      Source:Computers & Mathematics with Applications
      Author(s): F. Dassi, L. Mascotto
      We present numerical tests of the virtual element method (VEM) tailored for the discretization of a three dimensional Poisson problem with high-order “polynomial” degree (up to p = 10 ). Besides, we discuss possible reasons for which the method could return suboptimal/wrong error convergence curves. Among these motivations, we highlight ill-conditioning of the stiffness matrix and not particularly “clever” choices of the stabilizations. We propose variants of the definition of face/bulk degrees of freedom, as well as of stabilizations, which lead to methods that are much more robust in terms of numerical performances.

      PubDate: 2018-02-26T06:08:30Z
      DOI: 10.1016/j.camwa.2018.02.005
       
  • Improvement of third-order WENO-Z scheme at critical points
    • Authors: Weizheng Xu; Weiguo Wu
      Abstract: Publication date: Available online 22 February 2018
      Source:Computers & Mathematics with Applications
      Author(s): Weizheng Xu, Weiguo Wu
      In this paper, we present an improved third-order WENO-Z scheme to improve the order of convergence at critical points. This scheme is constructed through slightly modifying the local smoothness indicators of the conventional WENO-Z scheme with the way of Taylor expansion for third-order convergence. The present scheme is proved to be close to third-order by several standard accuracy tests. The performance enhancement of the WENO scheme through this modification is verified on a variety of one-dimensional and two-dimensional standard numerical experiments. Numerical results indicate that the present scheme provides better results in comparison with the earlier third-order WENO schemes like WENO-JS3, WENO-Z3.

      PubDate: 2018-02-26T06:08:30Z
      DOI: 10.1016/j.camwa.2018.02.009
       
  • Rational and semi-rational solutions of the y-nonlocal
           Davey–Stewartson I equation
    • Authors: Chao Qian; Jiguang Rao; Dumitru Mihalache; Jingsong He
      Abstract: Publication date: Available online 22 February 2018
      Source:Computers & Mathematics with Applications
      Author(s): Chao Qian, Jiguang Rao, Dumitru Mihalache, Jingsong He
      The nonlocal Davey–Stewartson (DS) I equation with a parity-time-symmetric potential with respect to the y -direction, which is called the y -nonlocal DS I equation, is a two-dimensional analogue of the nonlocal nonlinear Schrödinger (NLS) equation. The multi-breather solutions for the y -nonlocal DS I equation are derived by using the Hirota bilinear method. Lump-type solutions and hybrid solutions consisting of lumps sitting on periodic line waves are generated by long wave limits of the obtained soliton solutions. Also, various types of analytical solutions for the nonlocal NLS equation with negative nonlinearity, including both the Akhmediev breathers and the Peregrine rogue waves sitting on periodic line waves, can be generated with appropriate constraints on the parameters of the obtained exact solutions of the y -nonlocal DS I equation. Particularly, we show that a family of hybrid solitons describing the Peregrine rogue wave that coexists with the Akhmediev breather, both of them sitting on a spatially-periodic background can be thus obtained.

      PubDate: 2018-02-26T06:08:30Z
      DOI: 10.1016/j.camwa.2018.01.049
       
  • Orthogonal spline collocation method for the fourth-order diffusion system
    • Authors: Xuehua Yang; Haixiang Zhang; Da Xu
      Abstract: Publication date: Available online 21 February 2018
      Source:Computers & Mathematics with Applications
      Author(s): Xuehua Yang, Haixiang Zhang, Da Xu
      The fourth-order diffusion systems depict the wave and photon propagation in intense laser beams and play an important role in the phase separation in binary mixture. In this paper, by using orthogonal spline collocation (OSC) method in spatial direction and classical L1 approximation in temporal direction, a fully discrete scheme is established for a class of fourth-order fractional reaction–diffusion equations. For the original unknown u and auxiliary variable v = Δ u , the full-discrete unconditional stabilities based on a priori analysis are derived by virtue of properties of OSC. Moreover, the convergence rates in L 2 -norm for unknown u are strictly investigated. At the same time, the optimal error estimates in H 1 -norm for unknown u and in L 2 -norm for variable v , are also derived, respectively. For further verifying the theoretical analysis, some numerical examples are provided.

      PubDate: 2018-02-26T06:08:30Z
      DOI: 10.1016/j.camwa.2018.01.039
       
  • Godunov-type upwind flux schemes of the two-dimensional finite volume
           discrete Boltzmann method
    • Authors: Leitao Chen; Laura Schaefer
      Abstract: Publication date: Available online 21 February 2018
      Source:Computers & Mathematics with Applications
      Author(s): Leitao Chen, Laura Schaefer
      A simple unified Godunov-type upwind approach that does not need Riemann solvers for the flux calculation is developed for the finite volume discrete Boltzmann method (FVDBM) on an unstructured cell-centered triangular mesh. With piecewise-constant (PC), piecewise-linear (PL) and piecewise-parabolic (PP) reconstructions, three Godunov-type upwind flux schemes with different orders of accuracy are subsequently derived. After developing both a semi-implicit time marching scheme tailored for the developed flux schemes, and a versatile boundary treatment that is compatible with all of the flux schemes presented in this paper, numerical tests are conducted on spatial accuracy for several single-phase flow problems. Four major conclusions can be made. First, the Godunov-type schemes display higher spatial accuracy than the non-Godunov ones as the result of a more advanced treatment of the advection. Second, the PL and PP schemes are much more accurate than the PC scheme for velocity solutions. Third, there exists a threshold spatial resolution below which the PL scheme is better than the PP scheme and above which the PP scheme becomes more accurate. Fourth, besides increasing spatial resolution, increasing temporal resolution can also improve the accuracy in space for the PL and PP schemes.

      PubDate: 2018-02-26T06:08:30Z
      DOI: 10.1016/j.camwa.2018.01.034
       
  • Infinitely many solutions and least energy solutions for
           Klein–Gordon–Maxwell systems with general superlinear nonlinearity
    • Authors: Sitong Chen; Xianhua Tang
      Abstract: Publication date: Available online 19 February 2018
      Source:Computers & Mathematics with Applications
      Author(s): Sitong Chen, Xianhua Tang
      This paper is concerned with the following Klein–Gordon–Maxwell system: − △ u + V ( x ) u − ( 2 ω + ϕ ) ϕ u = f ( x , u ) , x ∈ R 3 , △ ϕ = ( ω + ϕ ) u 2 , x ∈ R 3 , where ω > 0 is a constant, V ∈ C ( R 3 , R ) , f ∈ C ( R 3 × R , R ) , and f is superlinear at infinity. Using some weaker superlinear conditions instead of the common super-cubic conditions on f , we prove that the above system has (1) infinitely many solutions when V ( x ) is coercive and sign-changing; (2) a least energy solution when V ( x ) is positive periodic. These results improve the related ones in the literature.

      PubDate: 2018-02-26T06:08:30Z
      DOI: 10.1016/j.camwa.2018.02.004
       
  • A symbolic computation approach to constructing rogue waves with a
           controllable center in the nonlinear systems
    • Authors: Zhaqilao
      Abstract: Publication date: Available online 19 February 2018
      Source:Computers & Mathematics with Applications
      Author(s): Zhaqilao
      A symbolic computation approach to constructing higher order rogue waves with a controllable center of the nonlinear systems is presented, making use of their Hirota bilinear forms. As some examples, it turns out that some higher order rogue wave solutions of the Kadomtsev–Petviashvili (KP) type equations in ( 3 + 1 ) and ( 2 + 1 ) -dimensions are obtained. Some features of controllable center of rogue waves are graphically discussed.

      PubDate: 2018-02-26T06:08:30Z
       
  • Variants of the deteriorated PSS preconditioner for saddle point problems
    • Authors: Zhao-Zheng Liang; Guo-Feng Zhang
      Abstract: Publication date: Available online 19 February 2018
      Source:Computers & Mathematics with Applications
      Author(s): Zhao-Zheng Liang, Guo-Feng Zhang
      Two new preconditioners, which can be viewed as variants of the deteriorated positive definite and skew-Hermitian splitting preconditioner, are proposed for solving saddle point problems. The corresponding iteration methods are proved to be convergent unconditionally for cases with positive definite leading blocks. The choice strategies of optimal parameters for the two iteration methods are discussed based on two recent optimization results for extrapolated Cayley transform, which result in faster convergence rate and more clustered spectrum. Compared with some preconditioners of similar structures, the new preconditioners have better convergence properties and spectrum distributions. In addition, more practical preconditioning variants of the new preconditioners are considered. Numerical experiments are presented to illustrate the advantages of the new preconditioners over some similar preconditioners to accelerate GMRES.

      PubDate: 2018-02-26T06:08:30Z
      DOI: 10.1016/j.camwa.2018.01.030
       
  • The Drazin inverse of an even-order tensor and its application to singular
           tensor equations
    • Authors: Jun Ji; Yimin Wei
      Abstract: Publication date: Available online 19 February 2018
      Source:Computers & Mathematics with Applications
      Author(s): Jun Ji, Yimin Wei
      The notion of the Moore–Penrose inverses of matrices was recently extended from matrix space to even-order tensor space with Einstein product in the literature. In this paper, we further study the properties of even-order tensors with Einstein product. We define the index and characterize the invertibility of an even-order square tensor. We also extend the notion of the Drazin inverse of a square matrix to an even-order square tensor. An expression for the Drazin inverse through the core-nilpotent decomposition for a tensor of even-order is obtained. As an application, the Drazin inverse solution of the singular linear tensor equation A ∗ X = B will also be included.

      PubDate: 2018-02-26T06:08:30Z
      DOI: 10.1016/j.camwa.2018.02.006
       
  • Periodic solutions for a class of evolution inclusions
    • Authors: Nikolaos Papageorgiou
      Abstract: Publication date: Available online 17 February 2018
      Source:Computers & Mathematics with Applications
      Author(s): Nikolaos S. Papageorgiou, Vicenţiu D. Rădulescu, Dušan D. Repovš
      We consider a periodic evolution inclusion defined on an evolution triple of spaces. The inclusion involves also a subdifferential term. We prove existence theorems for both the convex and the nonconvex problem, and we also produce extremal trajectories. Moreover, we show that every solution of the convex problem can be approximated uniformly by certain extremal trajectories (strong relaxation). We illustrate our results by examining a nonlinear parabolic control system.

      PubDate: 2018-02-26T06:08:30Z
       
  • Energy decay rate for a von Karman system with a boundary nonlinear delay
           term
    • Authors: Daewook Kim; Jong Yeoul Park; Yong Han Kang
      Abstract: Publication date: Available online 16 February 2018
      Source:Computers & Mathematics with Applications
      Author(s): Daewook Kim, Jong Yeoul Park, Yong Han Kang
      In this paper, we show the energy decay rate for a von Karman system with a boundary nonlinear delay term. This work is devoted to investigate the influence of kernel function g and the effect of the boundary nonlinear term μ 1 u t ( t ) m − 1 u t ( t ) , a boundary nonlinear time delay term μ 2 u t ( t − τ ) m − 1 u t ( t − τ ) and prove energy decay rates of solutions when g do not necessarily decay exponentially and the boundary condition has a time delay.

      PubDate: 2018-02-26T06:08:30Z
      DOI: 10.1016/j.camwa.2018.01.046
       
  • Simplifying biochemical tumorous bone remodeling models through variable
           order derivatives
    • Authors: Joana P. Neto; Rui Moura Coelho; Duarte Valério; Susana Vinga; Dominik Sierociuk; Wiktor Malesza; Michal Macias; Andrzej Dzieliński
      Abstract: Publication date: Available online 16 February 2018
      Source:Computers & Mathematics with Applications
      Author(s): Joana P. Neto, Rui Moura Coelho, Duarte Valério, Susana Vinga, Dominik Sierociuk, Wiktor Malesza, Michal Macias, Andrzej Dzieliński
      Bone is a living tissue that is constantly being renewed, where different cell types can induce a remodeling action to its structure. These mechanisms are typically represented through differential equations, accounting for the biochemical coupling between osteoclastic and osteoblastic cells. Remodeling models have also been extended to include the effects of tumorous disruptive pathologies in the bone dynamics. This article provides a novel approach to existing biochemical models, acting on two different stages. First, the models are said to physiologically better explain an osteolytic metastatic disease to the bone than the multiple myeloma previously considered. Second, and most importantly, variable order derivatives were introduced, for the first time in biochemical bone remodeling models. This resulted in a set of equations with less parameters that describe tumorous remodeling, and provide similar results to those of the original formulation. A more compact model, that promptly highlights tumorous bone interactions, is then achieved. Comparison of simulations and parameters is provided. Such results are a one-step-closer insight to, in a near future, easily provide clinical decision systems ensuring tailored personalized therapy schemes, for more efficient and targeted therapies.

      PubDate: 2018-02-26T06:08:30Z
      DOI: 10.1016/j.camwa.2018.01.037
       
  • A generalized element-free Galerkin method for Stokes problem
    • Authors: Tao Zhang; Xiaolin Li
      Abstract: Publication date: Available online 16 February 2018
      Source:Computers & Mathematics with Applications
      Author(s): Tao Zhang, Xiaolin Li
      A generalized element-free Galerkin (GEFG) method is developed in this paper for solving Stokes problem in primitive variable form. To obtain stable numerical results for both velocity and pressure, extended terms are only introduced into the approximate space of velocity in a special way as that in the generalized finite element method. Theoretical analysis shows that the GEFG method implies a stabilized formulation similar to that in the variational multiscale element-free Galerkin (VMEFG) method. Numerical results show the efficiency of the present method and reveal that both computational errors and CPU times of the present method are less than those of the VMEFG and the finite element methods.

      PubDate: 2018-02-26T06:08:30Z
      DOI: 10.1016/j.camwa.2018.01.035
       
  • A semi analytical method for the free vibration of doubly-curved shells of
           revolution
    • Authors: Fuzhen Pang; Haichao Li; Xueren Wang; Xuhong Miao; Shuo Li
      Abstract: Publication date: Available online 16 February 2018
      Source:Computers & Mathematics with Applications
      Author(s): Fuzhen Pang, Haichao Li, Xueren Wang, Xuhong Miao, Shuo Li
      In this paper, a semi analytical method is used to investigate the free vibration of doubly-curved shells of revolution with arbitrary boundary conditions. The doubly-curved shells of revolution are divided into their segments in the meridional direction, and the theoretical model for vibration analysis is formulated by applying Flügge’s thin shell theory. Regardless of the boundary conditions, the displacement functions of shell segments are composed by the Jacobi polynomials along the revolution axis direction and the standard Fourier series along the circumferential direction. The boundary conditions at the ends of the doubly-curved shells of revolution and the continuous conditions at two adjacent segments were enforced by the penalty method. Then, the natural frequencies of the doubly-curved shells are obtained by using the Rayleigh–Ritz method. For arbitrary boundary conditions, this method does not require any changes to the mathematical model or the displacement functions, and it is very effective in the analysis of free vibration for doubly-curved shells of revolution. The credibility and exactness of proposed method are compared with the results of finite element method (FEM), and some numerical results are reported for free vibration of the doubly-curved shells of revolution under classical and elastic boundary conditions. Results of this paper can provide reference data for future studies in related field.

      PubDate: 2018-02-26T06:08:30Z
      DOI: 10.1016/j.camwa.2018.01.045
       
  • A multigrid optimization algorithm for the numerical solution of
           quasilinear variational inequalities involving the p-Laplacian
    • Authors: Sergio
      Abstract: Publication date: 15 February 2018
      Source:Computers & Mathematics with Applications, Volume 75, Issue 4
      Author(s): Sergio González-Andrade, Sofía López-Ordóñez
      In this paper we propose a multigrid optimization algorithm (MG/OPT) for the numerical solution of a class of quasilinear variational inequalities of the second kind. This approach is enabled by the fact that the solution of the variational inequality is given by the minimizer of a nonsmooth energy functional, involving the p -Laplace operator. We propose a Huber regularization of the functional and a finite element discretization for the problem. Further, we analyze the regularity of the discretized energy functional, and we are able to prove that its Jacobian is slantly differentiable. This regularity property is useful to analyze the convergence of the MG/OPT algorithm. In fact, we demonstrate that the algorithm is globally convergent by using a mean value theorem for semismooth functions. Finally, we apply the MG/OPT algorithm to the numerical simulation of the viscoplastic flow of Bingham, Casson and Herschel–Bulkley fluids in a pipe. Several experiments are carried out to show the efficiency of the proposed algorithm when solving this kind of fluid mechanics problems.

      PubDate: 2018-02-26T06:08:30Z
       
  • Dynamical behavior of a general reaction–diffusion–advection model for
           two competing species
    • Authors: Tang
      Abstract: Publication date: 15 February 2018
      Source:Computers & Mathematics with Applications, Volume 75, Issue 4
      Author(s): De Tang, Li Ma
      It is well known that the studies of the evolution of biased movement along a resource gradient could create very interesting phenomena. This paper deals with a general two-species Lotka–Volterra competition model for the same resources in an advective nonhomogeneous environment, where the individuals are exposed to unidirectional flow (advection) but no individuals are lost through the boundary. It is assumed that the two species have the same population dynamics but different diffusion and advection rates. It is shown that at least five scenarios can occur (i) If one with a very strong biased movement relative to diffusion and the other with a more balanced approach, the species with much larger advection dispersal rate is driven to extinction; (ii) If one with a very strong biased movement and the other is smaller compare to its diffusion, the two species can coexist since one species mainly pursues resources at places of locally most favorable environments while the other relies on resources from other parts of the habitat; (iii) If both of the species random dispersal rates are sufficiently large (respectively small), two competing species coexist; (iv) If one with a sufficiently large random dispersal rate and the other with a sufficiently small one, two competing species still coexist; (v) If one with a sufficiently small random dispersal rate and the other with a suitable diffusion, which causes the extinction of the species with smaller random movement. Where (iii), (iv) and (v) show the global dynamics of (5) when both of the species dispersal rates are sufficiently large or sufficiently small. These results provide a new mechanism for the coexistence of competing species, and they also imply that selection is against excessive advection along environmental gradients (respectively, random dispersal rate), and an intermediate biased movement rate (respectively, random dispersal rate) may evolve. Finally, we also apply a perturbation argument to illustrate the evolution of these rates.

      PubDate: 2018-02-26T06:08:30Z
       
  • PDE formulation of some SABR/LIBOR market models and its numerical
           solution with a sparse grid combination technique
    • Authors: Carlos
      Abstract: Publication date: Available online 30 December 2017
      Source:Computers & Mathematics with Applications
      Author(s): José G. López-Salas, Carlos Vázquez
      SABR models have been used to incorporate stochastic volatility to LIBOR market models (LMM) in order to describe interest rate dynamics and price interest rate derivatives. From the numerical point of view, the pricing of derivatives with SABR/LIBOR market models (SABR/LMMs) is mainly carried out with Monte Carlo simulation. However, this approach could involve excessively long computational times. For first time in the literature, in the present paper we propose an alternative pricing based on partial differential equations (PDEs). Thus, we pose original PDE formulations associated to the SABR/LMMs proposed by Hagan and Lesniewsk (2008), Mercurio and Morini (2009) and Rebonato and White (2008). Moreover, as the PDEs associated to these SABR/LMMs are high dimensional in space, traditional full grid methods (like standard finite differences or finite elements) are not able to price derivatives over more than three or four underlying interest rates. In order to overcome this curse of dimensionality, a sparse grid combination technique is proposed. A comparison between Monte Carlo simulation results and the ones obtained with the sparse grid technique illustrates the performance of the method.

      PubDate: 2018-02-05T05:41:11Z
       
  • Lattice Boltzmann method based on Dual-MRT model for three-dimensional
           natural convection and entropy generation in CuO–water nanofluid filled
           cuboid enclosure included with discrete active walls
    • Authors: Alireza Rahimi; Abbas Kasaeipoor Ali Amiri Mohammad Hossein Doranehgard Emad
      Abstract: Publication date: Available online 29 December 2017
      Source:Computers & Mathematics with Applications
      Author(s): Alireza Rahimi, Abbas Kasaeipoor, Ali Amiri, Mohammad Hossein Doranehgard, Emad Hasani Malekshah, Lioua Kolsi
      In the present study, the three-dimensional natural convection and entropy generation in a cuboid enclosure included with various discrete active walls is analyzed using lattice Boltzmann method. The enclosure is filled with CuO–water nanofluid. To predict thermo-physical properties, dynamic viscosity and thermal conductivity, of CuO–water nanofluid, the KKL model is applied to consider the effect of Brownian motion on nanofluid properties. In lattice Boltzmann simulation, two different MRT models are used to solve the problem. The D3Q7-MRT model is used to solve the temperature filed, and the D3Q19 is employed to solve the fluid flow of natural convection within the enclosure. The influences of different Rayleigh numbers 1 0 3 < R a < 1 0 6 and solid volume fractions 0 < φ < 0 . 04 and four different arrangements of discrete active walls on the fluid flow, heat transfer, total entropy generation, local heat transfer irreversibility and local fluid friction irreversibility are presented comprehensively.

      PubDate: 2018-02-05T05:41:11Z
       
  • Entropy generation analysis and heatline visualization of free convection
           in nanofluid (KKL model-based)-filled cavity including internal active
           fins using lattice Boltzmann method
    • Authors: Alireza Rahimi; Mohammad Sepehr Milad Janghorban Lariche Abbas Kasaeipoor Emad
      Abstract: Publication date: Available online 29 December 2017
      Source:Computers & Mathematics with Applications
      Author(s): Alireza Rahimi, Mohammad Sepehr, Milad Janghorban Lariche, Abbas Kasaeipoor, Emad Hasani Malekshah, Lioua Kolsi
      Two-dimensional natural convection and entropy generation in a square cavity filled with CuO–water nanofluid is performed. The lattice Boltzmann method is employed to solve the problem numerically. The influences of different Rayleigh numbers 1 0 3 < R a < 1 0 6 and solid volume fractions 0 < φ < 0 . 05 on the fluid flow, heat transfer and total/local entropy generation are presented comprehensively. Also, the heatline visualization is employed to identify the heat energy flow. To predict the thermo-physical properties, dynamic viscosity and thermal conductivity, of CuO–water nanofluid, the KKL model is applied to consider the effect of Brownian motion on nanofluid properties. It is concluded that the configurations of active fins have pronounced effect on the fluid flow, heat transfer and entropy generation. Furthermore, the Nusselt number has direct relationship with Rayleigh number and solid volume fraction, and the entropy generation has direct and reverse relationships with Rayleigh number and solid volume fraction, respectively.

      PubDate: 2018-02-05T05:41:11Z
       
  • Convergence of an implicit–explicit midpoint scheme for
           computational micromagnetics
    • Authors: Dirk Praetorius; Michele Ruggeri Bernhard Stiftner
      Abstract: Publication date: Available online 28 December 2017
      Source:Computers & Mathematics with Applications
      Author(s): Dirk Praetorius, Michele Ruggeri, Bernhard Stiftner
      Based on lowest-order finite elements in space, we consider the numerical integration of the Landau–Lifschitz–Gilbert equation (LLG). The dynamics of LLG is driven by the so-called effective field which usually consists of the exchange field, the external field, and lower-order contributions such as the stray field. The latter requires the solution of an additional partial differential equation in full space. Following Bartels and Prohl (2006), we employ the implicit midpoint rule to treat the exchange field. However, in order to treat the lower-order terms effectively, we combine the midpoint rule with an explicit Adams–Bashforth scheme. The resulting integrator is formally of second-order in time, and we prove unconditional convergence towards a weak solution of LLG. Numerical experiments underpin the theoretical findings.

      PubDate: 2018-02-05T05:41:11Z
       
  • A method of harmonic extension for computing the generalized stress
           intensity factors for Laplace’s equation with singularities
    • Authors: A.A. Dosiyev
      Abstract: Publication date: Available online 26 December 2017
      Source:Computers & Mathematics with Applications
      Author(s): A.A. Dosiyev
      The solution of the Dirichlet problem for Laplace’s equation on a special polygon is harmonically extended to a sector with the center at the singular vertex. This is followed by an integral representation of the extended function in this sector, which is approximated by the mid-point rule. By using the extension properties for the approximate values at the quadrature nodes, a well-conditioned and exponentially convergent, with respect to the number of nodes algebraic system of equations are obtained. These values determine the coefficients of the series representation of the solution around the singular vertex of the polygonal domain, which are called the generalized stress intensity factors (GSIFs). The comparison of the results with those existing in the literature, in the case of Motz’s problem, show that the obtained GSIFs are more accurate. Moreover, the extremely accurate series segment solution is obtained by taking an appropriate number of calculated GSIFs.

      PubDate: 2017-12-27T11:44:35Z
       
  • On the fractional Schrödinger–Kirchhoff equations with electromagnetic
           fields and critical nonlinearity
    • Authors: Sihua Liang; Binlin Zhang
      Abstract: Publication date: Available online 26 December 2017
      Source:Computers & Mathematics with Applications
      Author(s): Sihua Liang, Dušan Repovš, Binlin Zhang
      In this paper, we consider the fractional Schrödinger–Kirchhoff equations with electromagnetic fields and critical nonlinearity ε 2 s M ( [ u ] s , A ε 2 ) ( − Δ ) A ε s u + V ( x ) u = u 2 s ∗ − 2 u + h ( x , u 2 ) u , x ∈ R N , u ( x ) → 0 , as x → ∞ , where ( − Δ ) A ε s is the fractional magnetic operator with 0 < s < 1 , 2 s ∗ = 2 N ∕ ( N − 2 s ) , M : R 0 + → R + is a continuous nondecreasing function, V : R N → R 0 + and A : R N → R N are the electric and magnetic potentials, respectively. By using the fractional version of the concentration compactness principle and variational methods, we show that the above problem: (i) has at least one solution provided that ε < E ; and (ii) for any m ∗ ∈ N , has m ∗ pairs of solutions if ε < E m ∗ , where E and E m ∗ are sufficiently small positive numbers. Moreover, these solutions u ...
      PubDate: 2017-12-27T11:44:35Z
       
  • A meshless average source boundary node method for steady-state heat
           conduction in general anisotropic media
    • Authors: Yao-Ming Zhang; Fang-Ling Sun Wen-Zhen Yan Der-Liang Young
      Abstract: Publication date: Available online 21 December 2017
      Source:Computers & Mathematics with Applications
      Author(s): Yao-Ming Zhang, Fang-Ling Sun, Wen-Zhen Qu, Yan Gu, Der-Liang Young
      The average source boundary node method (ASBNM) is a recent boundary-type meshless method, which uses only the boundary nodes in the solution procedure without involving any element or integration notion, that is truly meshless and easy to implement. This paper documents the first attempt to extend the ASBNM for solving the steady-state heat conduction problems in general anisotropic media. Noteworthily, for boundary-type meshless/meshfree methods which depend on the boundary integral equations, whatever their forms are, a key but difficult issue is to accurately and efficiently determine the diagonal coefficients of influence matrices. In this study, we develop a new scheme to evaluate the diagonal coefficients via the pure boundary node implementation based on coupling a new regularized boundary integral equation with direct unknowns of considered problems and the average source technique (AST). Seven two- and three-dimensional benchmark examples are tested in comparison with some existing methods. Numerical results demonstrate that the present ASBNM is superior in the light of overall accuracy, efficiency, stability and convergence rates, especially for the solution of the boundary quantities.

      PubDate: 2017-12-27T11:44:35Z
       
  • A posteriori error estimates of two-grid finite volume element methods for
           nonlinear elliptic problems
    • Authors: Chuanjun Chen; Yanping Chen Xin Zhao
      Abstract: Publication date: Available online 21 December 2017
      Source:Computers & Mathematics with Applications
      Author(s): Chuanjun Chen, Yanping Chen, Xin Zhao
      In this paper, we study the a posteriori error estimates of two-grid finite volume element method for second-order nonlinear elliptic equations. We derive the residual-based a posteriori error estimator and prove the computable upper and lower bounds on the error in H 1 -norm. The a posteriori error estimator can be used to assess the accuracy of the two-grid finite volume element solutions in practical applications. Numerical examples are provided to illustrate the performance of the proposed estimator.

      PubDate: 2017-12-27T11:44:35Z
       
  • Global asymptotic stability of steady states in a chemotaxis-growth system
           with singular sensitivity
    • Authors: Pan Zheng; Chunlai Robert Willie Xuegang
      Abstract: Publication date: Available online 16 December 2017
      Source:Computers & Mathematics with Applications
      Author(s): Pan Zheng, Chunlai Mu, Robert Willie, Xuegang Hu
      This paper deals with a fully parabolic chemotaxis-growth system with singular sensitivity u t = Δ u − χ ∇ ⋅ u ∇ ln v + r u − μ u 2 , ( x , t ) ∈ Ω × ( 0 , ∞ ) , v t = Δ v − v + u , ( x , t ) ∈ Ω × ( 0 , ∞ ) , under homogeneous Neumann boundary conditions in a smooth bounded domain Ω ⊂ R 2 , where the parameters χ , μ > 0 and r ∈ R . Global existence and boundedness of solutions to the above system were established under some suitable conditions by Zhao and Zheng (2017). The main aim of this paper is further to show the large time behavior of global solutions which cannot be derived in the previous work.

      PubDate: 2017-12-27T11:44:35Z
       
 
 
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