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  Subjects -> MATHEMATICS (Total: 909 journals)
    - APPLIED MATHEMATICS (75 journals)
    - GEOMETRY AND TOPOLOGY (20 journals)
    - MATHEMATICS (676 journals)
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    - NUMERICAL ANALYSIS (19 journals)
    - PROBABILITIES AND MATH STATISTICS (78 journals)

MATHEMATICS (676 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: 16)
ACM Transactions on Computational Logic (TOCL)     Hybrid Journal   (Followers: 4)
ACM Transactions on Mathematical Software (TOMS)     Hybrid Journal   (Followers: 6)
ACS Applied Materials & Interfaces     Full-text available via subscription   (Followers: 25)
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: 7)
Advances in Computational Mathematics     Hybrid Journal   (Followers: 15)
Advances in Decision Sciences     Open Access   (Followers: 5)
Advances in Difference Equations     Open Access   (Followers: 2)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 11)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 2)
Advances in Materials Sciences     Open Access   (Followers: 16)
Advances in Mathematical Physics     Open Access   (Followers: 5)
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: 11)
Advances in Porous Media     Full-text available via subscription   (Followers: 4)
Advances in Pure and Applied Mathematics     Hybrid Journal   (Followers: 6)
Advances in Pure Mathematics     Open Access   (Followers: 4)
Advances in Science and Research (ASR)     Open Access   (Followers: 6)
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: 9)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Al-Jabar : Jurnal Pendidikan Matematika     Open Access  
Algebra and Logic     Hybrid Journal   (Followers: 4)
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: 4)
American Journal of Mathematical Analysis     Open Access  
American Journal of Mathematics     Full-text available via subscription   (Followers: 7)
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: 7)
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: 3)
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: 8)
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)
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: 12)
Applied Mathematics     Open Access   (Followers: 3)
Applied Mathematics     Open Access   (Followers: 5)
Applied Mathematics & Optimization     Hybrid Journal   (Followers: 4)
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: 1)
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 5)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 3)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 5)
Archive of Numerical Software     Open Access  
Archives of Computational Methods in Engineering     Hybrid Journal   (Followers: 4)
Arkiv för Matematik     Hybrid Journal   (Followers: 1)
Arnold Mathematical Journal     Hybrid Journal   (Followers: 1)
Artificial Satellites : The Journal of Space Research Centre of Polish Academy of Sciences     Open Access   (Followers: 21)
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: 7)
Australian Primary Mathematics Classroom     Full-text available via subscription   (Followers: 3)
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  
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 the Brazilian Mathematical Society, New Series     Hybrid Journal  
Bulletin of the London Mathematical Society     Hybrid Journal   (Followers: 3)
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: 20)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal   (Followers: 1)
CHANCE     Hybrid Journal   (Followers: 6)
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: 2)
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: 3)
COMBINATORICA     Hybrid Journal  
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: 1)
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: 9)
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: 4)
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: 6)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
Contributions to Game Theory and Management     Open Access  
COSMOS     Hybrid Journal  
Cryptography and Communications     Hybrid Journal   (Followers: 14)
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: 11)
Demonstratio Mathematica     Open Access  
Dependence Modeling     Open Access  
Design Journal : An International Journal for All Aspects of Design     Hybrid Journal   (Followers: 28)
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 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)
Energy for Sustainable Development     Hybrid Journal   (Followers: 9)
Enseñanza de las Ciencias : Revista de Investigación y Experiencias Didácticas     Open Access  
Ensino da Matemática em Debate     Open Access  
Entropy     Open Access   (Followers: 5)
ESAIM: Control Optimisation and Calculus of Variations     Full-text available via subscription   (Followers: 1)
European Journal of Combinatorics     Full-text available via subscription   (Followers: 5)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)

        1 2 3 4 | Last

Journal Cover Applied Numerical Mathematics
  [SJR: 1.254]   [H-I: 56]   [5 followers]  Follow
    
   Hybrid Journal Hybrid journal (It can contain Open Access articles)
   ISSN (Print) 0168-9274 - ISSN (Online) 0168-9274
   Published by Elsevier Homepage  [3118 journals]
  • Computing eigenvalues and eigenfunctions of the Laplacian for convex
           polygons
    • Authors: Matthew J. Colbrook; Athanasisos S. Fokas
      Pages: 1 - 17
      Abstract: Publication date: April 2018
      Source:Applied Numerical Mathematics, Volume 126
      Author(s): Matthew J. Colbrook, Athanasisos S. Fokas
      Recently a new transform method, called the Unified Transform or the Fokas method, for solving boundary value problems (BVPs) for linear and integrable nonlinear partial differential equations (PDEs) has received a lot of attention. For linear elliptic PDEs, this method yields two equations, known as the global relations, coupling the Dirichlet and Neumann boundary values. These equations can be used in a collocation method to determine the Dirichlet to Neumann map. This involves expanding the unknown functions in terms of a suitable basis, and choosing a set of collocation points at which to evaluate the global relations. Here, using these methods for the Helmholtz and modified Helmholtz equations and following the earlier results of [15], we determine eigenvalues of the Laplacian in a convex polygon. Eigenvalues are characterised by the points where the generalised Dirichlet to Neumann map becomes singular. We find that the method yields spectral convergence for eigenfunctions smooth on the boundary and for non-smooth boundary values, the rate of convergence is determined by the rate of convergence of expansions in the chosen Legendre basis. Extensions to the case of oblique derivative boundary conditions and constant coefficient elliptic PDEs are also discussed and demonstrated.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.12.001
      Issue No: Vol. 126 (2017)
       
  • Efficient approaches for enclosing the united solution set of the interval
           generalized Sylvester matrix equations
    • Authors: Marzieh Dehghani-Madiseh; Milan Hladík
      Pages: 18 - 33
      Abstract: Publication date: April 2018
      Source:Applied Numerical Mathematics, Volume 126
      Author(s): Marzieh Dehghani-Madiseh, Milan Hladík
      We investigate the interval generalized Sylvester matrix equation A X B + C X D = F . We propose a necessary condition for its solutions, and also a sufficient condition for boundedness of the whole solution set. The main effort is performed to develop techniques for computing outer estimations of the so-called united solution set of this interval system. First, we propose a modified variant of the Krawczyk operator, reducing significantly computational complexity, compared to the Kronecker product form. We then propose an iterative technique for enclosing the solution set. These approaches are based on spectral decompositions of the midpoints of A, B, C and D and in both of them we suppose that the midpoints of A and C are simultaneously diagonalizable as well as for the midpoints of the matrices B and D. Numerical experiments are given to illustrate the performance of the proposed methods.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.12.003
      Issue No: Vol. 126 (2017)
       
  • An explicit spectral collocation method for the linearized Korteweg–de
           Vries equation on unbounded domain
    • Authors: Jinwei Fang; Boying Wu; Wenjie Liu
      Pages: 34 - 52
      Abstract: Publication date: April 2018
      Source:Applied Numerical Mathematics, Volume 126
      Author(s): Jinwei Fang, Boying Wu, Wenjie Liu
      In this paper, we present a stable and efficient numerical scheme for the linearized Korteweg–de Vries equation on unbounded domain. After employing the Crank–Nicolson method for temporal discretization, the transparent boundary conditions are derived for the time semi-discrete scheme. Then the unconditional stability of the resulting initial boundary problem is established. For spatial discretization, we construct a non-polynomial based spectral collocation method in which the basis functions are built upon a generalized Birkhoff interpolation. The interpolation error of the new basis is also investigated. Moreover, the basis functions build in two free parameters intrinsically which can be chosen properly so that the implicit time semi-discrete scheme collapses to an explicit scheme after spatial discretization. Numerical tests are performed to demonstrate the stability and accuracy of the proposed method.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.11.008
      Issue No: Vol. 126 (2017)
       
  • Analysis of a dynamic contact problem with nonmonotone friction and
           non-clamped boundary conditions
    • Authors: Mikael Barboteu; Krzysztof Bartosz; David Danan
      Pages: 53 - 77
      Abstract: Publication date: April 2018
      Source:Applied Numerical Mathematics, Volume 126
      Author(s): Mikael Barboteu, Krzysztof Bartosz, David Danan
      We consider a dynamic process of frictional contact between a non-clamped viscoelastic body and a foundation. We assume that the normal contact response depends on the depth of penetration of the foundation by the considered body, and the dependence between these two quantities is governed by normal compliance conditions. On the other hand, the friction force is assumed to be a nonmonotone function of the slip rate where the friction threshold also depends on the depth of the penetration. Our aim in this paper is twofold. The first one is to prove the existence and the uniqueness of a weak solution for the contact problem under consideration. The second one is to provide the numerical analysis of the process involving its semi-discrete and fully discrete approximation as well as estimation of the error for both numerical schemes and the validation of such a result.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.12.005
      Issue No: Vol. 126 (2017)
       
  • Increasing the approximation order of the triangular Shepard method
    • Authors: F. Dell'Accio; F. Di Tommaso; O. Nouisser; B. Zerroudi
      Pages: 78 - 91
      Abstract: Publication date: April 2018
      Source:Applied Numerical Mathematics, Volume 126
      Author(s): F. Dell'Accio, F. Di Tommaso, O. Nouisser, B. Zerroudi
      In this paper we discuss an improvement of the triangular Shepard operator proposed by Little to extend the Shepard method. In particular, we use triangle based basis functions in combination with a modified version of the linear local interpolant on the vertices of the triangle. We deeply study the resulting operator, which uses functional and derivative data, has cubic approximation order and a good accuracy of approximation. Suggestions on how to avoid the use of derivative data, without losing both order and accuracy of approximation, are given.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.12.006
      Issue No: Vol. 126 (2017)
       
  • Parameter selection for HOTV regularization
    • Authors: Toby Sanders
      Pages: 1 - 9
      Abstract: Publication date: March 2018
      Source:Applied Numerical Mathematics, Volume 125
      Author(s): Toby Sanders
      Popular methods for finding regularized solutions to inverse problems include sparsity promoting ℓ 1 regularization techniques, one in particular which is the well known total variation (TV) regularization. More recently, several higher order (HO) methods similar to TV have been proposed, which we generally refer to as HOTV methods. In this letter, we investigate the problem of the often debated selection of λ, the parameter used to carefully balance the interplay between data fitting and regularization terms. We theoretically argue for a scaling of the operators for a uniform parameter selection for all orders of HOTV regularization. In particular, parameter selection for all orders of HOTV may be determined by scaling an initial parameter for TV, which the imaging community may be more familiar with. We also provide several numerical results which justify our theoretical findings.

      PubDate: 2017-11-09T09:57:16Z
      DOI: 10.1016/j.apnum.2017.10.010
      Issue No: Vol. 125 (2017)
       
  • A pseudospectral scheme and its convergence analysis for high-order
           integro-differential equations
    • Authors: Xiaojun Tang; Heyong Xu
      Pages: 51 - 67
      Abstract: Publication date: March 2018
      Source:Applied Numerical Mathematics, Volume 125
      Author(s): Xiaojun Tang, Heyong Xu
      The main purpose of this work is to develop an integral pseudospectral scheme for solving integro-differential equations. We provide new pseudospectral integration matrices (PIMs) for the Legendre–Gauss and the flipped Legendre–Gauss–Radau points, respectively, and present an efficient and stable approach to computing the PIMs via the recursive calculation of Legendre integration matrices. Furthermore, we provide a rigorous convergence analysis for the proposed pseudospectral scheme in both L ∞ and L 2 spaces via a linear integral equation, and the spectral rate of convergence is demonstrated by numerical results.

      PubDate: 2017-11-16T11:59:56Z
      DOI: 10.1016/j.apnum.2017.10.003
      Issue No: Vol. 125 (2017)
       
  • Fast computation of stationary joint probability distribution of sparse
           Markov chains
    • Authors: Weiyang Ding; Michael Ng; Yimin Wei
      Pages: 68 - 85
      Abstract: Publication date: March 2018
      Source:Applied Numerical Mathematics, Volume 125
      Author(s): Weiyang Ding, Michael Ng, Yimin Wei
      In this paper, we study a fast algorithm for finding stationary joint probability distributions of sparse Markov chains or multilinear PageRank vectors which arise from data mining applications. In these applications, the main computational problem is to calculate and store solutions of many unknowns in joint probability distributions of sparse Markov chains. Our idea is to approximate large-scale solutions of such sparse Markov chains by two components: the sparsity component and the rank-one component. Here the non-zero locations in the sparsity component refer to important associations in the joint probability distribution and the rank-one component refers to a background value of the solution. We propose to determine solutions by formulating and solving sparse and rank-one optimization problems via closed form solutions. The convergence of the truncated power method is established. Numerical examples of multilinear PageRank vector calculation and second-order web-linkage analysis are presented to show the efficiency of the proposed method. It is shown that both computation and storage are significantly reduced by comparing with the traditional power method.

      PubDate: 2017-11-16T11:59:56Z
      DOI: 10.1016/j.apnum.2017.10.008
      Issue No: Vol. 125 (2017)
       
  • Quadratic/linear rational spline collocation for linear boundary value
           problems
    • Authors: Erge Ideon; Peeter Oja
      Pages: 143 - 158
      Abstract: Publication date: March 2018
      Source:Applied Numerical Mathematics, Volume 125
      Author(s): Erge Ideon, Peeter Oja
      We investigate the collocation method with quadratic/linear rational spline S of smoothness class C 2 for the numerical solution of two-point boundary value problems if the solution y (or −y) of the boundary value problem is a strictly convex function. We show that on the uniform mesh it holds ‖ S − y ‖ ∞ = O ( h 2 ) . Established bound of error gives a dependence on the solution of the boundary value problem and its coefficient functions. We prove also convergence rates ‖ S ′ − y ′ ‖ ∞ = O ( h 2 ) and ‖ S ″ − y ″ ‖ ∞ = O ( h 2 ) . Numerical examples support the obtained theoretical results.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.11.005
      Issue No: Vol. 125 (2017)
       
  • The second order perturbation approach for elliptic partial differential
           equations on random domains
    • Authors: Helmut Harbrecht; Michael D. Peters
      Pages: 159 - 171
      Abstract: Publication date: March 2018
      Source:Applied Numerical Mathematics, Volume 125
      Author(s): Helmut Harbrecht, Michael D. Peters
      The present article is dedicated to the solution of elliptic boundary value problems on random domains. We apply a high-precision second order shape Taylor expansion to quantify the impact of the random perturbation on the solution. Thus, we obtain a representation of the solution with third order accuracy in the size of the perturbation's amplitude. The major advantage of this approach is that we end up with purely deterministic equations for the solution's moments. In particular, we derive representations for the first four moments, i.e., expectation, variance, skewness and kurtosis. These moments are efficiently computable by means of boundary integral equations. Numerical results are presented to validate the presented approach.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.11.002
      Issue No: Vol. 125 (2017)
       
  • A discrete divergence free weak Galerkin finite element method for the
           Stokes equations
    • Authors: Lin Mu; Junping Wang; Xiu Ye; Shangyou Zhang
      Pages: 172 - 182
      Abstract: Publication date: March 2018
      Source:Applied Numerical Mathematics, Volume 125
      Author(s): Lin Mu, Junping Wang, Xiu Ye, Shangyou Zhang
      A discrete divergence free weak Galerkin finite element method is developed for the Stokes equations based on a weak Galerkin (WG) method introduced in [17]. Discrete divergence free bases are constructed explicitly for the lowest order weak Galerkin elements in two and three dimensional spaces. These basis functions can be derived on general meshes of arbitrary shape of polygons and polyhedrons. With the divergence free basis derived, the discrete divergence free WG scheme can eliminate pressure variable from the system and reduces a saddle point problem to a symmetric and positive definite system with many fewer unknowns. Numerical results are presented to demonstrate the robustness and accuracy of this discrete divergence free WG method.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.11.006
      Issue No: Vol. 125 (2017)
       
  • Conforming finite element methods for the stochastic
           Cahn–Hilliard–Cook equation
    • Authors: Shimin Chai; Yanzhao Cao; Yongkui Zou; Wenju Zhao
      Pages: 44 - 56
      Abstract: Publication date: February 2018
      Source:Applied Numerical Mathematics, Volume 124
      Author(s): Shimin Chai, Yanzhao Cao, Yongkui Zou, Wenju Zhao
      This paper is concerned with the finite element approximation of the stochastic Cahn–Hilliard–Cook equation driven by an infinite dimensional Wiener type noise. The Argyris finite elements are used to discretize the spatial variables while the infinite dimensional (cylindrical) Wiener process is approximated by truncated stochastic series spanned by the spectral basis of the covariance operator. The optimal strong convergence order in L 2 and H ˙ − 2 norms is obtained. Unlike the mixed finite element method studied in the existing literature, our method allows the covariance operator of the Wiener process to have an infinite trace, including the space–time white noise is allowed in our model. Numerical experiments are presented to illustrate the theoretical analysis.

      PubDate: 2017-10-25T12:06:02Z
      DOI: 10.1016/j.apnum.2017.09.010
      Issue No: Vol. 124 (2017)
       
  • A high-order fully conservative block-centered finite difference method
           for the time-fractional advection–dispersion equation
    • Authors: Xiaoli Li; Hongxing Rui
      Pages: 89 - 109
      Abstract: Publication date: February 2018
      Source:Applied Numerical Mathematics, Volume 124
      Author(s): Xiaoli Li, Hongxing Rui
      Based on the weighted and shifted Grünwald–Letnikov difference operator, a new high-order block-centered finite difference method is derived for the time-fractional advection–dispersion equation by introducing an auxiliary flux variable to guarantee full mass conservation. The stability and the global convergence of the scheme are proved rigorously. Some a priori estimates of discrete norms with optimal order of convergence O ( Δ t 3 + h 2 + k 2 ) both for solute concentration and the auxiliary flux variable are established on non-uniform rectangular grids, where Δ t ,   h and k are the step sizes in time, space in x- and y-direction. Moreover, the applicability and accuracy of the scheme are demonstrated by numerical experiments to support our theoretical analysis.

      PubDate: 2017-11-02T09:17:53Z
      DOI: 10.1016/j.apnum.2017.10.004
      Issue No: Vol. 124 (2017)
       
  • The fictitious domain method with H1-penalty for the Stokes problem with
           Dirichlet boundary condition
    • Authors: Guanyu Zhou
      Pages: 1 - 21
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Guanyu Zhou
      We consider the fictitious domain method with H 1 -penalty for the Stokes problem with Dirichlet boundary condition. First, for the continuous penalty problem, we obtain the optimal error estimate O ( ϵ ) for both the velocity and pressure, where ϵ is the penalty parameter. Moreover, we investigate the H m -regularity for the solution of the penalty problem. Then, we apply the finite element method with the P1/P1 element to the penalty problem. Since the solution to the penalty problem has a jump in the traction vector, we introduce some interpolation/projection operators, as well as an inf-sup condition with the norm depending on ϵ. With the help of these preliminaries, we derive the error estimates for the finite element approximation. The theoretical results are verified by the numerical experiments.

      PubDate: 2017-09-26T13:37:25Z
      DOI: 10.1016/j.apnum.2017.08.005
      Issue No: Vol. 123 (2017)
       
  • Implicit–Explicit WENO scheme for the equilibrium dispersive model
           of chromatography
    • Authors: R. Donat; F. Guerrero; P. Mulet
      Pages: 22 - 42
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): R. Donat, F. Guerrero, P. Mulet
      Chromatographic processes can be modeled by nonlinear, convection-dominated partial differential equations, together with nonlinear relations: the adsorption isotherms. In this paper we consider the nonlinear equilibrium dispersive (ED) model with adsorption isotherms of Langmuir type. We show that, in this case, the ED model can be written as a system of conservation laws when the dispersion coefficient vanishes. We also show that the function that relates the conserved variables and the physically observed concentrations of the components in the mixture is one to one and it admits a global inverse, which cannot be given explicitly, but can be adequately computed. As a result, fully conservative numerical schemes can be designed for the ED model in chromatography. We propose a Weighted-Essentially-non-Oscillatory second order IMEX scheme and describe the numerical issues involved in its application. Through a series of numerical experiments, we show that our scheme gives accurate numerical solutions which capture the sharp discontinuities present in the chromatographic fronts, with the same stability restrictions as in the purely hyperbolic case.

      PubDate: 2017-09-26T13:37:25Z
      DOI: 10.1016/j.apnum.2017.08.008
      Issue No: Vol. 123 (2017)
       
  • Fractional PDE constrained optimization: An optimize-then-discretize
           approach with L-BFGS and approximate inverse preconditioning
    • Authors: Stefano Cipolla; Fabio Durastante
      Pages: 43 - 57
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Stefano Cipolla, Fabio Durastante
      In this paper, using an optimize-then-discretize approach, we address the numerical solution of two Fraction Partial Differential Equation constrained optimization problems: the Fractional Advection Dispersion Equation (FADE) and the two-dimensional semilinear Riesz Space Fractional Diffusion equation. Both a theoretical and experimental analysis of the problem is carried out. The algorithmic framework is based on the L-BFGS method coupled with a Krylov subspace solver. A suitable preconditioning strategy by approximate inverses is taken into account. Graphics Processing Unit (GPU) accelerator is used in the construction of the preconditioners. The numerical experiments are performed with benchmarked software/libraries enforcing the reproducibility of the results.

      PubDate: 2017-09-26T13:37:25Z
      DOI: 10.1016/j.apnum.2017.09.001
      Issue No: Vol. 123 (2017)
       
  • Algorithms for the implementation of adaptive isogeometric methods using
           hierarchical B-splines
    • Authors: Eduardo M. Garau; Rafael Vázquez
      Pages: 58 - 87
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Eduardo M. Garau, Rafael Vázquez
      In this article we introduce all the ingredients to develop adaptive isogeometric methods based on hierarchical B-splines. In particular, we give precise definitions of local refinement and coarsening that, unlike previously existing methods, can be understood as the inverse of each other. We also define simple and intuitive data structures for the implementation of hierarchical B-splines, and algorithms for refinement and coarsening that take advantage of local information. We complete the paper with some simple numerical tests to show the performance of the data structures and algorithms, that have been implemented in the open-source Octave/Matlab code GeoPDEs.

      PubDate: 2017-09-26T13:37:25Z
      DOI: 10.1016/j.apnum.2017.08.006
      Issue No: Vol. 123 (2017)
       
  • Supercloseness of the continuous interior penalty method for singularly
           perturbed problems in 1D: Vertex-cell interpolation
    • Authors: Jin Zhang; Xiaowei Liu
      Pages: 88 - 98
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Jin Zhang, Xiaowei Liu
      A continuous interior penalty method with piecewise polynomials of degree p ≥ 2 is applied on a Shishkin mesh to solve a singularly perturbed convection–diffusion problem, whose solution has a single boundary layer. This method is analyzed by means of a series of integral identities developed for the convection terms. Then we prove a supercloseness bound of order 5/2 for a vertex-cell interpolation when p = 2 . The sharpness of our analysis is supported by some numerical experiments. Moreover, numerical tests show supercloseness clearly for p ≥ 3 .

      PubDate: 2017-09-26T13:37:25Z
      DOI: 10.1016/j.apnum.2017.09.003
      Issue No: Vol. 123 (2017)
       
  • Fully spectral collocation method for nonlinear parabolic partial
           integro-differential equations
    • Authors: Farhad Fakhar-Izadi; Mehdi Dehghan
      Pages: 99 - 120
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Farhad Fakhar-Izadi, Mehdi Dehghan
      The numerical approximation of solution to nonlinear parabolic Volterra and Fredholm partial integro-differential equations is studied in this paper. Unlike the conventional methods which discretize the time variable by finite difference schemes, we use the spectral method for this purpose. Indeed, both of the space and time discretizations are based on the Legendre-collocation method which lead to conversion of the problem to a nonlinear system of algebraic equations. The convergence of the proposed method is proven by providing an L ∞ error estimate. Several numerical examples are included to demonstrate the efficiency and spectral accuracy of the proposed method in the space and time directions.

      PubDate: 2017-10-03T14:25:01Z
      DOI: 10.1016/j.apnum.2017.08.007
      Issue No: Vol. 123 (2017)
       
  • Solving a class of nonlinear boundary integral equations based on the
           meshless local discrete Galerkin (MLDG) method
    • Authors: Pouria Assari; Mehdi Dehghan
      Pages: 137 - 158
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Pouria Assari, Mehdi Dehghan
      The main purpose of this article is to investigate a computational scheme for solving a class of nonlinear boundary integral equations which occurs as a reformulation of boundary value problems of Laplace's equations with nonlinear Robin boundary conditions. The method approximates the solution by the Galerkin method based on the use of moving least squares (MLS) approach as a locally weighted least square polynomial fitting. The discrete Galerkin method for solving boundary integral equations results from the numerical integration of all integrals appeared in the method. The numerical scheme developed in the current paper utilizes the non-uniform Gauss–Legendre quadrature rule to estimate logarithm-like singular integrals. Since the proposed method is constructed on a set of scattered points, it does not require any background mesh and so we can call it as the meshless local discrete Galerkin (MLDG) method. The scheme is simple and effective to solve boundary integral equations and its algorithm can be easily implemented. We also obtain the error bound and the convergence rate of the presented method. Finally, numerical examples are included to show the validity and efficiency of the new technique and confirm the theoretical error estimates.

      PubDate: 2017-10-03T14:25:01Z
      DOI: 10.1016/j.apnum.2017.09.002
      Issue No: Vol. 123 (2017)
       
  • On order conditions for modified Patankar–Runge–Kutta schemes
    • Authors: S. Kopecz; A. Meister
      Pages: 159 - 179
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): S. Kopecz, A. Meister
      In [6] the modified Patankar–Euler and modified Patankar–Runge–Kutta schemes were introduced to solve positive and conservative systems of ordinary differential equations. These modifications of the forward Euler scheme and Heun's method guarantee positivity and conservation irrespective of the chosen time step size. In this paper we introduce a general definition of modified Patankar–Runge–Kutta schemes and derive necessary and sufficient conditions to obtain first and second order methods. We also introduce two novel families of two-stage second order modified Patankar–Runge–Kutta schemes.

      PubDate: 2017-10-03T14:25:01Z
      DOI: 10.1016/j.apnum.2017.09.004
      Issue No: Vol. 123 (2017)
       
  • Weak Galerkin mixed finite element method for heat equation
    • Authors: Chenguang Zhou; Yongkui Zou; Shimin Chai; Qian Zhang; Hongze Zhu
      Pages: 180 - 199
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Chenguang Zhou, Yongkui Zou, Shimin Chai, Qian Zhang, Hongze Zhu
      In this paper, we apply a new weak Galerkin mixed finite element method (WGMFEM) with stabilization term to solve heat equations. This method allows the usage of totally discontinuous functions in the approximation space. The WGMFEM is capable of providing very accurate numerical approximations for both the primary and flux variables. In addition, we develop and analyze the error estimates for both continuous and discontinuous time WGMFEM schemes. Optimal order error estimates in both L 2 and triple-bar ⫼ ⋅ ⫼ norms are established, respectively. Finally, numerical tests are conducted to illustrate the theoretical results.

      PubDate: 2017-10-03T14:25:01Z
      DOI: 10.1016/j.apnum.2017.08.009
      Issue No: Vol. 123 (2017)
       
  • On the partial condition numbers for the indefinite least squares problem
    • Authors: Hanyu Li; Shaoxin Wang
      Pages: 200 - 220
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Hanyu Li, Shaoxin Wang
      The condition number of a linear function of the indefinite least squares solution is called the partial condition number for the indefinite least squares problem. In this paper, based on a new and very general condition number which can be called the unified condition number, we first present an expression of the partial unified condition number when the data space is measured by a general weighted product norm. Then, by setting the specific norms and weight parameters, we obtain the expressions of the partial normwise, mixed and componentwise condition numbers. Moreover, the corresponding structured partial condition numbers are also taken into consideration when the problem is structured. Considering the connections between the indefinite and total least squares problems, we derive the (structured) partial condition numbers for the latter, which generalize the ones in the literature. To estimate these condition numbers effectively and reliably, the probabilistic spectral norm estimator and the small-sample statistical condition estimation method are applied and three related algorithms are devised. Finally, the obtained results are illustrated by numerical experiments.

      PubDate: 2017-10-03T14:25:01Z
      DOI: 10.1016/j.apnum.2017.09.006
      Issue No: Vol. 123 (2017)
       
  • Numerical simulation of Bloch equations for dynamic magnetic resonance
           imaging
    • Authors: Arijit Hazra; Gert Lube; Hans-Georg Raumer
      Pages: 241 - 255
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Arijit Hazra, Gert Lube, Hans-Georg Raumer
      Magnetic Resonance Imaging (MRI) is a widely applied non-invasive imaging modality based on non-ionizing radiation which gives excellent images and soft tissue contrast of living tissues. We consider the modified Bloch problem as a model of MRI for flowing spins in an incompressible flow field. After establishing the well-posedness of the corresponding evolution problem, we analyze its spatial semi-discretization using discontinuous Galerkin methods. The high frequency time evolution requires a proper explicit and adaptive temporal discretization. The applicability of the approach is shown for basic examples.

      PubDate: 2017-10-11T14:37:22Z
      DOI: 10.1016/j.apnum.2017.09.007
      Issue No: Vol. 123 (2017)
       
  • Analysis of a velocity–stress–pressure formulation for a
           fluid–structure interaction problem
    • Authors: María González; Virginia Selgas
      Pages: 275 - 299
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): María González, Virginia Selgas
      We consider a fluid–structure interaction problem consisting of the time-dependent Stokes equations in the fluid domain coupled with the equations of linear elastodynamics in the solid domain. For simplicity, all changes of geometry are neglected. We propose a new method in terms of the fluid velocity, the fluid pressure, the structural velocity and the Cauchy stress tensor. We show that the new weak formulation is well-posed. Then, we propose a new semidiscrete problem where the velocities and the fluid pressure are approximated using a stable pair for the Stokes problem in the fluid domain and compatible finite elements in the solid domain. We obtain a priori estimates for the solution of the semidiscrete problem, prove the convergence of these solutions to the solution of the weak formulation and obtain error estimates. A time discretization based on the backward Euler method leads to a fully discrete scheme in which the computation of the approximated Cauchy stress tensor can be decoupled from that of the remaining unknowns at each time step. The displacements in the structure (if needed) can be recovered by quadrature. Finally, some numerical experiments showing the performance of the method are provided.

      PubDate: 2017-10-11T14:37:22Z
      DOI: 10.1016/j.apnum.2017.09.011
      Issue No: Vol. 123 (2017)
       
  • A lagged diffusivity method for reaction–convection–diffusion
           equations with Dirichlet boundary conditions
    • Authors: Francesco Mezzadri; Emanuele Galligani
      Pages: 300 - 319
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Francesco Mezzadri, Emanuele Galligani
      In this paper we solve a 2D nonlinear, non-steady reaction–convection–diffusion equation subject to Dirichlet boundary conditions by an iterative procedure consisting in lagging the diffusion term. First, we analyze the procedure, which we call Lagged Diffusivity Method. In particular, we provide a proof of the uniqueness of the solution and of the convergence of the lagged iteration when some assumptions are satisfied. We also describe outer and inner solvers, with special regard to how to link the stopping criteria in an efficient way. Numerical experiments are then introduced in order to evaluate the role of different linear solvers and of other components of the solution procedure, considering also the effect of the discretization.

      PubDate: 2017-10-11T14:37:22Z
      DOI: 10.1016/j.apnum.2017.09.009
      Issue No: Vol. 123 (2017)
       
  • Line integral solution of Hamiltonian systems with holonomic constraints
    • Authors: Luigi Brugnano; Gianmarco Gurioli; Felice Iavernaro; Ewa B. Weinmüller
      Abstract: Publication date: Available online 24 December 2017
      Source:Applied Numerical Mathematics
      Author(s): Luigi Brugnano, Gianmarco Gurioli, Felice Iavernaro, Ewa B. Weinmüller
      In this paper, we propose a second-order energy-conserving approximation procedure for Hamiltonian systems with holonomic constraints. The derivation of the procedure relies on the use of the so-called line integral framework. We provide numerical experiments to illustrate theoretical findings.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.12.014
       
  • An hp-version error analysis of the discontinuous Galerkin method for
           linear elasticity
    • Authors: Jianguo Huang; Xuehai Huang
      Abstract: Publication date: Available online 21 December 2017
      Source:Applied Numerical Mathematics
      Author(s): Jianguo Huang, Xuehai Huang
      An hp-version error analysis is developed for the general DG method in mixed formulation for solving the linear elastic problem. First of all, we give the hp-version error estimates of two L 2 projection operators. Then incorporated with the techniques in [11], we obtain the hp-version error estimates in energy norm and L 2 norm. Some numerical experiments are provided for demonstrating the theoretical results.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.12.010
       
  • Criteria for hexahedral cell classification
    • Authors: Olga V. Ushakova
      Abstract: Publication date: Available online 20 December 2017
      Source:Applied Numerical Mathematics
      Author(s): Olga V. Ushakova
      The aim of the paper is to give the numerical criteria for classification of different types of hexahedral cells which can emerge in a three-dimensional structured grid generation. In general, computational grids and their cells have to be nondegenerate, however, in practice, situations arise in which degenerate grids are used and computed. In these cases, to prevent lost of accuracy, special strategies must be chosen both in grid generation and physical phenomenon solution algorithms. To determine which cells need a modification in above strategies, degenerate cells have to be detected. The criteria are suggested for hexahedral cells constructed by a trilinear mapping of the unit cube. All hexahedral cells are divided into nondegenerate and degenerate. Among nondegenerate hexahedral cells, cells exotic in shape are singled out as inadmissible. Degenerate cells are divided into pyramids, prisms and tetrahedrons—types of cells which can be admissible in grid generation and solution algorithms. Inadmissible types of degenerations are also considered. An algorithm for testing three-dimensional structured grids according to suggested criteria is described. Both results of testing and examples of different types of cells are demonstrated. In conclusion, recommendations for structured grid generation with the purpose to exclude undesirable types of cells are given.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.12.012
       
  • A conforming enriched finite element method for elliptic interface
           problems
    • Authors: Hua Wang; Jinru Chen; Pengtao Sun; Fangfang Qin
      Abstract: Publication date: Available online 20 December 2017
      Source:Applied Numerical Mathematics
      Author(s): Hua Wang, Jinru Chen, Pengtao Sun, Fangfang Qin
      A new conforming enriched finite element method is presented for elliptic interface problems with interface-unfitted meshes. The conforming enriched finite element space is constructed based on the P 1 -conforming finite element space. Approximation capability of the conforming enriched finite element space is analyzed. The standard conforming Galerkin method is considered without any penalty stabilization term. Our method does not limit the diffusion coefficient of the elliptic interface problem to a piecewise constant. Finite element errors in H 1 -norm and L 2 -norm are proved to be optimal. Numerical experiments are carried out to validate theoretical results.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.12.011
       
  • Shape optimization for Stokes flows using sensitivity analysis and finite
           element method
    • Authors: V.C. Le; H.T. Pham; T.T.M. Ta
      Abstract: Publication date: Available online 20 December 2017
      Source:Applied Numerical Mathematics
      Author(s): V.C. Le, H.T. Pham, T.T.M. Ta
      In the context of structural optimization in fluid mechanics we propose a numerical method based on a combination of the classical shape derivative and Hadamard's boundary variation method. Our approach regards the viscous flows governed by Stokes equations with the objective function of energy dissipation and a constrained volume. The shape derivative is computed by Lagrange's approach via the solutions of Stokes and adjoint systems. The programs are written in FreeFem++ using the Finite Element method.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.12.009
       
  • Discrete Modified Projection Method for Urysohn Integral Equations with
           Smooth Kernels
    • Authors: Rekha P. Kulkarni; Gobinda Rakshit
      Abstract: Publication date: Available online 18 December 2017
      Source:Applied Numerical Mathematics
      Author(s): Rekha P. Kulkarni, Gobinda Rakshit
      Approximate solutions of linear and nonlinear integral equations using methods related to an interpolatory projection involve many integrals which need to be evaluated using a numerical quadrature formula. In this paper, we consider discrete versions of the modified projection method and of the iterated modified projection method for solution of a Urysohn integral equation with a smooth kernel. For r ≥ 1 , a space of piecewise polynomials of degree ≤ r − 1 with respect to an uniform partition is chosen to be the approximating space and the projection is chosen to be the interpolatory projection at r Gauss points. The orders of convergence which we obtain for these discrete versions indicate the choice of numerical quadrature which preserves the orders of convergence. Numerical results are given for a specific example.

      PubDate: 2017-12-27T08:27:00Z
      DOI: 10.1016/j.apnum.2017.12.008
       
  • Error analysis of the high order scheme for homogenization of
           Hamilton–Jacobi equation
    • Authors: Xinpeng Yuan; Chunguang Xiong Guoqing Zhu
      Abstract: Publication date: Available online 14 December 2017
      Source:Applied Numerical Mathematics
      Author(s): Xinpeng Yuan, Chunguang Xiong, Guoqing Zhu
      In this paper, employing ideas developed for conservation law equations such as the Lax–Friedrich-type and Godunov-type numerical fluxes, we describe the numerical schemes for approximating the solution of the limit problem arising in the homogenization of Hamilton–Jacobi equations. All approximation methods involve three steps. The first scheme is a provably monotonic discretization of the cell problem for approximating the effective Hamiltonian for a given vector P ∈ R N . Next, using interpolation, we present an approximation of the effective Hamiltonian in the domain R N . Finally, the numerical schemes of the Hamilton–Jacobi equations with the effective Hamiltonian approximation are constructed. We also present global error estimates including all the discrete mesh sizes. The theoretical results are illustrated through numerical examples, including two convex Hamiltonians and two non-convex Hamiltonians.

      PubDate: 2017-12-27T08:27:00Z
       
  • Mixed recurrence equations and interlacing properties for zeros of
           sequences of classical q-orthogonal polynomials
    • Authors: D.D. Tcheutia; A.S. Jooste; W. Koepf
      Abstract: Publication date: Available online 14 November 2017
      Source:Applied Numerical Mathematics
      Author(s): D.D. Tcheutia, A.S. Jooste, W. Koepf
      Using the q-version of Zeilberger's algorithm, we provide a procedure to find mixed recurrence equations satisfied by classical q-orthogonal polynomials with shifted parameters. These equations are used to investigate interlacing properties of zeros of sequences of q-orthogonal polynomials. In the cases where zeros do not interlace, we give some numerical examples to illustrate this.

      PubDate: 2017-11-16T11:59:56Z
      DOI: 10.1016/j.apnum.2017.11.003
       
  • The Crank-Nicolson/Adams-Bashforth scheme for the Burgers equation with H2
           and H1 initial data
    • Authors: Tong Zhang; JiaoJiao Jin; YuGao HuangFu
      Abstract: Publication date: Available online 10 November 2017
      Source:Applied Numerical Mathematics
      Author(s): Tong Zhang, JiaoJiao Jin, YuGao HuangFu
      In this paper, we consider the stability and convergence results of the Crank-Nicolson/Adams-Bashforth scheme for the Burgers equation with smooth and nonsmooth initial data. The spatial approximation is based on the standard conforming finite element space. The temporal treatment of the spatial discrete Burgers equation is based on the implicit Crank-Nicolson scheme for the linear term and the explicit Adams-Bashforth scheme for the nonlinear term. Firstly, we prove that the Crank-Nicolson/Adams-Bashforth scheme is almost unconditionally stable with initial data u 0 ∈ H α ( α = 1 , 2 ) . Secondly, the optimal error estimates of the numerical solution in L 2 -norm are derived with initial data u 0 ∈ H 2 , and the error estimates of approximate solution in L 2 norm obtained with initial data u 0 ∈ H 1 is reduced by 1 2 . Finally, some numerical examples are provided to verify the established stability theory and convergence results with H 2 and H 1 initial data.

      PubDate: 2017-11-16T11:59:56Z
      DOI: 10.1016/j.apnum.2017.10.009
       
  • The matrix splitting based proximal fixed-point algorithms for
           quadratically constrained ℓ1 minimization and Dantzig selector
    • Authors: Yongchao Yu; Jigen Peng
      Abstract: Publication date: Available online 3 November 2017
      Source:Applied Numerical Mathematics
      Author(s): Yongchao Yu, Jigen Peng
      This paper studies algorithms for solving quadratically constrained ℓ 1 minimization and Dantzig selector which have recently been widely used to tackle sparse recovery problems in compressive sensing. The two optimization models can be reformulated via two indicator functions as special cases of a general convex composite model which minimizes the sum of two convex functions with one composed with a matrix operator. The general model can be transformed into a fixed-point problem for a nonlinear operator which is composed of a proximity operator and an expansive matrix operator, and then a new iterative scheme based on the expansive matrix splitting is proposed to find fixed-points of the nonlinear operator. We also give some mild conditions to guarantee that the iterative sequence generated by the scheme converges to a fixed-point of the nonlinear operator. Further, two specific proximal fixed-point algorithms based on the scheme are developed and then applied to quadratically constrained ℓ 1 minimization and Dantzig selector. Numerical results have demonstrated that the proposed algorithms are comparable to the state-of-the-art algorithms for recovering sparse signals with different sizes and dynamic ranges in terms of both accuracy and speed. In addition, we also extend the proposed algorithms to solve two harder constrained total-variation minimization problems.

      PubDate: 2017-11-09T09:57:16Z
      DOI: 10.1016/j.apnum.2017.11.001
       
  • Splitting schemes for unsteady problems involving the grad-div operator
    • Authors: Peter Minev; Petr N. Vabishchevich
      Abstract: Publication date: Available online 31 October 2017
      Source:Applied Numerical Mathematics
      Author(s): Peter Minev, Petr N. Vabishchevich
      In this paper we consider various splitting schemes for unsteady problems containing the grad-div operator. The fully implicit discretization of such problems would yield at each time step a linear problem that couples all components of the solution vector. In this paper we discuss various possibilities to decouple the equations for the different components that result in unconditionally stable schemes. If the spatial discretization uses Cartesian grids, the resulting schemes are Locally One Dimensional (LOD). The stability analysis of these schemes is based on the general stability theory of additive operator-difference schemes developed by Samarskii and his collaborators. The results of the theoretical analysis are illustrated on a 2D numerical example with a smooth manufactured solution.

      PubDate: 2017-11-02T09:17:53Z
      DOI: 10.1016/j.apnum.2017.10.005
       
  • Residual error estimation for anisotropic Kirchhoff plates
    • Authors: Michael Weise
      Abstract: Publication date: Available online 31 October 2017
      Source:Applied Numerical Mathematics
      Author(s): Michael Weise
      Residual error estimation for conforming finite element discretisations of the isotropic Kirchhoff plate problem is covered by an estimator of Verfürth for the related biharmonic equation. This article generalises Verfürth's result to Kirchhoff plates with an anisotropic material, which requires some modifications. Special emphasis is laid on the reduced Hsieh–Clough–Tocher triangular finite element, the conforming element with the least possible number of unknowns.

      PubDate: 2017-11-02T09:17:53Z
      DOI: 10.1016/j.apnum.2017.10.007
       
  • Differential equations for families of semi-classical orthogonal
           polynomials within class one
    • Authors: G. Filipuk; M.N. Rebocho
      Abstract: Publication date: Available online 23 October 2017
      Source:Applied Numerical Mathematics
      Author(s): G. Filipuk, M.N. Rebocho
      In this paper we study families of semi-classical orthogonal polynomials within class one. We derive general second or third order ordinary differential equations (with respect to certain parameters) for the recurrence coefficients of the three-term recurrence relation of these polynomials and show that in particular well-known cases, e.g. related to the modified Airy and Laguerre weights, these equations can be reduced to the second and the fourth Painlevé equations.

      PubDate: 2017-10-25T12:06:02Z
      DOI: 10.1016/j.apnum.2017.10.002
       
  • A new quadrature scheme based on an Extended Lagrange Interpolation
           process
    • Authors: Donatella Occorsio; Maria Grazia Russo
      Abstract: Publication date: Available online 18 October 2017
      Source:Applied Numerical Mathematics
      Author(s): Donatella Occorsio, Maria Grazia Russo
      Let w ( x ) = e − x β x α , w ¯ ( x ) = x w ( x ) and let { p m ( w ) } m , { p m ( w ¯ ) } m be the corresponding sequences of orthonormal polynomials. Since the zeros of p m + 1 ( w ) interlace those of p m ( w ¯ ) , it makes sense to construct an interpolation process essentially based on the zeros of Q 2 m + 1 : = p m + 1 ( w ) p m ( w ¯ ) , which is called “Extended Lagrange Interpolation". In this paper the convergence of this interpolation process is studied in suitable weighted L 1 spaces, in a general framework which completes the results given by the same authors in weighted L u p ( ( 0 , + ∞ ) ) , 1 ≤ p ≤ ∞ (see [30], [27]). As an application of the theoretical results, an extended product integration rule, based on the aforesaid Lagrange process, is proposed in order to compute integrals of the type ∫ 0 + ∞ f ( x ) k ( x , y ) u ( x ) d x , u ( x ) = e − x β x γ ( 1 + x ) λ , γ > − 1 , λ ∈ R + , where the kernel k ( x , y ) can be of different kinds. The rule, which is stable and fast convergent, is used in order to construct a computational scheme involving the single product integration rule studied in [22]. It is shown that the “compound quadrature sequence” represents an efficient proposal for saving 1/3 of the evaluations of the function f, under unchanged speed of convergence.
      PubDate: 2017-10-25T12:06:02Z
       
  • Stability and convergence analysis of a Crank-Nicolson leap-frog scheme
           for the unsteady incompressible Navier-Stokes equations
    • Authors: Qili Tang; Yunqing Huang
      Abstract: Publication date: Available online 12 October 2017
      Source:Applied Numerical Mathematics
      Author(s): Qili Tang, Yunqing Huang
      A fully discrete Crank-Nicolson leap-frog (CNLF) scheme is presented and studied for the nonstationary incompressible Navier-Stokes equations. The proposed scheme deals with the spatial discretization by Galerkin finite element method (FEM), treats the temporal discretization by CNLF method for the linear term and the semi-implicit method for nonlinear term. The almost unconditional stability, i.e., the time step is no more than a constant, is proven. By a new negative norm technique, the L 2 -optimal error estimates with respect to temporal and spacial orientation for the velocity are derived. At last, some numerical results are provided to justify our theoretical analysis.

      PubDate: 2017-10-18T15:25:02Z
      DOI: 10.1016/j.apnum.2017.09.012
       
  • On the discretization and application of two space–time boundary
           integral equations for 3D wave propagation problems in unbounded domains
    • Authors: Falletta Monegato; Scuderi
      Abstract: Publication date: February 2018
      Source:Applied Numerical Mathematics, Volume 124
      Author(s): S. Falletta, G. Monegato, L. Scuderi
      In this paper, we consider 3D wave propagation problems in unbounded domains, such as those of acoustic waves in non viscous fluids, or of seismic waves in (infinite) homogeneous isotropic materials, where the propagation velocity c is much higher than 1. For example, in the case of air and water c ≈ 343 m / s and c ≈ 1500 m / s respectively, while for seismic P-waves in linear solids we may have c ≈ 6000 m / s or higher. These waves can be generated by sources, possible away from the obstacles. We further assume that the dimensions of the obstacles are much smaller than that of the wave velocity, and that the problem transients are not excessively short. For their solution we consider two different approaches. The first directly uses a known space–time boundary integral equation to determine the problem solution. In the second one, after having defined an artificial boundary delimiting the region of computational interest, the above mentioned integral equation is interpreted as a non reflecting boundary condition to be coupled with a classical finite element method. For such problems, we show that in some cases the computational cost and storage, required by the above numerical approaches, can be significantly reduced by taking into account a property that till now has not been considered. To show the effectiveness of this reduction, the proposed approach is applied to several problems, including multiple scattering.

      PubDate: 2017-10-11T14:37:22Z
       
  • Spectral viscosity method with generalized Hermite functions for nonlinear
           conservation laws
    • Authors: Xue Luo
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Xue Luo
      In this paper, we propose new spectral viscosity methods based on the generalized Hermite functions for the solution of nonlinear scalar conservation laws in the whole line. It is shown rigorously that these schemes converge to the unique entropy solution by using compensated compactness arguments, under some conditions. The numerical experiments of the inviscid Burger's equation support our result, and it verifies the reasonableness of the conditions.

      PubDate: 2017-10-11T14:37:22Z
       
  • A plane-wave singularity subtraction technique for the classical Dirichlet
           and Neumann combined field integral equations
    • Authors: Carlos
      Abstract: Publication date: January 2018
      Source:Applied Numerical Mathematics, Volume 123
      Author(s): Carlos Pérez-Arancibia
      This paper presents expressions for the classical combined field integral equations for the solution of Dirichlet and Neumann exterior Helmholtz problems on the plane, in terms of smooth (continuously differentiable) integrands. These expressions are obtained by means of a singularity subtraction technique based on pointwise plane-wave expansions of the unknown density function. In particular, a novel regularization of the hypersingular operator is obtained, which, unlike regularizations based on Maue's integration-by-parts formula, does not give rise to involved Cauchy principal value integrals. Moreover, the expressions for the combined field integral operators and layer potentials presented in this contribution can be numerically evaluated at target points that are arbitrarily close to the boundary without severely compromising their accuracy. A variety of numerical examples in two spatial dimensions that consider three different Nyström discretizations for smooth domains and domains with corners—one of which is based on direct application of the trapezoidal rule—demonstrates the effectiveness of the proposed higher-order singularity subtraction approach.

      PubDate: 2017-10-03T14:25:01Z
       
  • A Continuous hp-mesh model for adaptive discontinuous Galerkin schemes
    • Authors: Vít Dolejší; Georg May; Ajay Rangarajan
      Abstract: Publication date: Available online 2 October 2017
      Source:Applied Numerical Mathematics
      Author(s): Vít Dolejší, Georg May, Ajay Rangarajan
      We present a continuous-mesh model for anisotropic hp-adaptation in the context of numerical methods using discontinuous piecewise polynomial approximation spaces. The present work is an extension of a previously proposed mesh-only (h-)adaptation method which uses both a continuous mesh, and a corresponding high-order continuous interpolation operator. In this previous formulation local anisotropy and global mesh density distribution may be determined by analytical optimization techniques, operating on the continuous mesh model. The addition of varying polynomial degree necessitates a departure from purely analytic optimization. However, we show in this article that a global optimization problem may still be formulated and solved by analytic optimization, adding only the necessity to solve numerically a single nonlinear algebraic equation per adaptation step to satisfy a constraint on the total number of degrees of freedom. The result is a tailorsuited continuous mesh with respect to a model for the global interpolation error measured in the L q -norm. From the continuous mesh a discrete triangular mesh may be generated using any metric-based mesh generator.

      PubDate: 2017-10-03T14:25:01Z
      DOI: 10.1016/j.apnum.2017.09.015
       
  • Analysis of Galerkin and streamline-diffusion FEMs on piecewise
           equidistant meshes for turning point problems exhibiting an interior layer
           
    • Authors: Simon Becher
      Abstract: Publication date: Available online 21 September 2017
      Source:Applied Numerical Mathematics
      Author(s): Simon Becher
      We consider singularly perturbed boundary value problems with a simple interior turning point whose solutions exhibit an interior layer. These problems are discretised using higher order finite elements on layer-adapted piecewise equidistant meshes proposed by Sun and Stynes. We also study the streamline-diffusion finite element method (SDFEM) for such problems. For these methods error estimates uniform with respect to ε are proven in the energy norm and in the stronger SDFEM-norm, respectively. Numerical experiments confirm the theoretical findings.

      PubDate: 2017-09-26T13:37:25Z
       
 
 
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