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  Subjects -> MATHEMATICS (Total: 879 journals)
    - APPLIED MATHEMATICS (71 journals)
    - GEOMETRY AND TOPOLOGY (19 journals)
    - MATHEMATICS (651 journals)
    - MATHEMATICS (GENERAL) (42 journals)
    - NUMERICAL ANALYSIS (19 journals)
    - PROBABILITIES AND MATH STATISTICS (77 journals)

MATHEMATICS (651 journals)                  1 2 3 4 | Last

Showing 1 - 200 of 538 Journals sorted alphabetically
Abakós     Open Access   (Followers: 3)
Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg     Hybrid Journal   (Followers: 2)
Academic Voices : A Multidisciplinary Journal     Open Access   (Followers: 2)
Accounting Perspectives     Full-text available via subscription   (Followers: 8)
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: 21)
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: 5)
Acta Mathematica Vietnamica     Hybrid Journal  
Acta Mathematicae Applicatae Sinica, English Series     Hybrid Journal  
Advanced Science Letters     Full-text available via subscription   (Followers: 7)
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: 4)
Advances in Difference Equations     Open Access   (Followers: 1)
Advances in Fixed Point Theory     Open Access   (Followers: 5)
Advances in Geosciences (ADGEO)     Open Access   (Followers: 10)
Advances in Linear Algebra & Matrix Theory     Open Access   (Followers: 1)
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: 5)
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: 7)
AKSIOMA Journal of Mathematics Education     Open Access   (Followers: 1)
Algebra and Logic     Hybrid Journal   (Followers: 3)
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 Biostatistics     Open Access   (Followers: 9)
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: 9)
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: 6)
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: 4)
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  
Applied Numerical Mathematics     Hybrid Journal   (Followers: 5)
Applied Spatial Analysis and Policy     Hybrid Journal   (Followers: 4)
Arab Journal of Mathematical Sciences     Open Access   (Followers: 2)
Arabian Journal of Mathematics     Open Access   (Followers: 2)
Archive for Mathematical Logic     Hybrid Journal   (Followers: 1)
Archive of Applied Mechanics     Hybrid Journal   (Followers: 4)
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: 19)
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: 2)
Australian Senior Mathematics Journal     Full-text available via subscription   (Followers: 1)
Automatic Documentation and Mathematical Linguistics     Hybrid Journal   (Followers: 5)
Axioms     Open Access  
Baltic International Yearbook of Cognition, Logic and Communication     Open Access  
Basin Research     Hybrid Journal   (Followers: 5)
BIBECHANA     Open Access  
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: 7)
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: 18)
Carpathian Mathematical Publications     Open Access   (Followers: 1)
Catalysis in Industry     Hybrid Journal   (Followers: 1)
CEAS Space Journal     Hybrid Journal  
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: 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: 2)
COMBINATORICA     Hybrid Journal  
Combustion Theory and Modelling     Hybrid Journal   (Followers: 13)
Commentarii Mathematici Helvetici     Hybrid Journal   (Followers: 1)
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: 5)
Concrete Operators     Open Access   (Followers: 4)
Confluentes Mathematici     Hybrid Journal  
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  
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: 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: 2)
Discrete Mathematics     Hybrid Journal   (Followers: 7)
Discrete Mathematics & Theoretical Computer Science     Open Access  
Discrete Mathematics, Algorithms and Applications     Hybrid Journal   (Followers: 2)
Discussiones Mathematicae Graph Theory     Open Access   (Followers: 1)
Dnipropetrovsk University Mathematics Bulletin     Open Access  
Doklady Mathematics     Hybrid Journal  
Duke Mathematical Journal     Full-text available via subscription   (Followers: 1)
Edited Series on Advances in Nonlinear Science and Complexity     Full-text available via subscription  
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: 3)
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: 4)
European Journal of Mathematics     Hybrid Journal   (Followers: 1)
European Scientific Journal     Open Access   (Followers: 2)
Experimental Mathematics     Hybrid Journal   (Followers: 4)
Expositiones Mathematicae     Hybrid Journal   (Followers: 2)
Facta Universitatis, Series : Mathematics and Informatics     Open Access  
Fasciculi Mathematici     Open Access  
Finite Fields and Their Applications     Full-text available via subscription   (Followers: 4)
Fixed Point Theory and Applications     Open Access   (Followers: 1)
Formalized Mathematics     Open Access   (Followers: 2)

        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  [3043 journals]
  • A posteriori error estimates and adaptivity for the discontinuous Galerkin
           solutions of nonlinear second-order initial-value problems
    • Authors: Mahboub Baccouch
      Pages: 18 - 37
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): Mahboub Baccouch
      In this paper, we propose and analyze an efficient and reliable a posteriori error estimator of residual-type for the discontinuous Galerkin (DG) method applied to nonlinear second-order initial-value problems for ordinary differential equations. This estimator is simple, efficient, and asymptotically exact. We use our recent optimal L 2 error estimates and superconvergence results of Baccouch [15] to show that the significant parts of the DG discretization errors are proportional to the ( p + 1 ) -degree right Radau polynomial, when polynomials of total degree not exceeding p are used. These new results allow us to construct a residual-based a posteriori error estimator which is obtained by solving a local residual problem with no initial condition on each element. We prove that, for smooth solutions, the proposed a posteriori error estimator converges to the actual error in the L 2 -norm with order of convergence p + 2 . Computational results indicate that the theoretical order of convergence is sharp. By adding the a posteriori error estimate to the DG solution, we obtain a post-processed approximation which superconverges with order p + 2 in the L 2 -norm. Moreover, we demonstrate the effectiveness of the this error estimator. Finally, we present a local adaptive mesh refinement (AMR) procedure that makes use of our local a posteriori error estimate. Our proofs are valid for arbitrary regular meshes and for P p polynomials with p ≥ 1 . Several numerical results are presented to validate the theoretical results.

      PubDate: 2017-07-02T16:25:43Z
      DOI: 10.1016/j.apnum.2017.06.001
      Issue No: Vol. 121 (2017)
       
  • Uncertainty quantification for linear hyperbolic equations with stochastic
           process or random field coefficients
    • Authors: Andrea Barth; Franz G. Fuchs
      Pages: 38 - 51
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): Andrea Barth, Franz G. Fuchs
      In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media. Two types of models are presented: The first has a time-dependent coefficient modeled by the Ornstein–Uhlenbeck process. The second has a random field coefficient with a given covariance in space. For the former a formula for the exact solution in terms of moments is derived. In both cases stable numerical schemes are introduced to solve these random partial differential equations. Simulation results including convergence studies conclude the theoretical findings.

      PubDate: 2017-07-12T12:47:24Z
      DOI: 10.1016/j.apnum.2017.06.009
      Issue No: Vol. 121 (2017)
       
  • A double-sided dynamic programming approach to the minimum time problem
           and its numerical approximation
    • Authors: Lars Grüne; Thuy T.T. Le
      Pages: 68 - 81
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): Lars Grüne, Thuy T.T. Le
      We introduce a new formulation of the minimum time problem in which we employ the signed minimum time function positive outside of the target, negative in its interior and zero on its boundary. Under some standard assumptions, we prove the so called Bridge Dynamic Programming Principle (BDPP) which is a relation between the value functions defined on the complement of the target and in its interior. Then owing to BDPP, we obtain the error estimates of a semi-Lagrangian discretization of the resulting Hamilton–Jacobi–Bellman equation. In the end, we provide numerical tests and error comparisons which show that the new approach can lead to significantly reduced numerical errors.

      PubDate: 2017-07-23T13:02:58Z
      DOI: 10.1016/j.apnum.2017.06.008
      Issue No: Vol. 121 (2017)
       
  • A new Crank–Nicolson finite element method for the time-fractional
           subdiffusion equation
    • Authors: Fanhai Zeng; Changpin Li
      Pages: 82 - 95
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): Fanhai Zeng, Changpin Li
      In this paper, a new Crank–Nicolson finite element method for the time-fractional subdiffusion equation is developed, in which a novel time discretization called the modified L1 method is used to discretize the Riemann–Liouville fractional derivative. The present method is unconditionally stable and convergent of order O ( τ 1 + β + h r + 1 ) , where β ∈ ( 0 , 1 ) , τ and h are the step sizes in time and space, respectively, and r is the degree of the piecewise polynomial space. The derived method is reduced to the classical Crank–Nicolson method when β → 1 . The new time discretization is also used to solve the fractional cable equation. And the unconditional stability and convergence are given. Numerical examples are provided which support the theoretical analysis. The comparison with the existing methods are also given, which shows good performances of the present methods.

      PubDate: 2017-07-23T13:02:58Z
      DOI: 10.1016/j.apnum.2017.06.011
      Issue No: Vol. 121 (2017)
       
  • Curvature-induced instability of a Stokes-like problem with non-standard
           boundary conditions
    • Authors: Armin Westerkamp; Manuel Torrilhon
      Pages: 96 - 114
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): Armin Westerkamp, Manuel Torrilhon
      We present an analysis of a set of parametrized boundary conditions for a Stokes–Brinkman model in two space dimensions, discretized by finite elements. We particularly point out an instability which arises when these boundary conditions are posed on a curved line, which then leads to unphysical oscillations. In contrast to a Navier-slip condition, which is prone to Babuška's paradox, this instability can be traced back to the continuous level. We claim that the stability in these cases depend on the amount of curvature at the boundary, which is shown in a reduced setting in cylinder coordinates. The transition to a two dimensional Cartesian case is then based on numerical studies, which further substantiate the claim. Lastly, stabilization techniques are motivated that enhance the continuous FEM setting and are conveniently able to deal with arising oscillations.

      PubDate: 2017-07-23T13:02:58Z
      DOI: 10.1016/j.apnum.2017.06.012
      Issue No: Vol. 121 (2017)
       
  • Second order accurate asynchronous scheme for modeling linear partial
           differential equations
    • Authors: Asma Toumi; Guillaume Dufour; Ronan Perrussel; Thomas Unfer
      Pages: 115 - 133
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): Asma Toumi, Guillaume Dufour, Ronan Perrussel, Thomas Unfer
      We propose an asynchronous method for the explicit integration of multi-scale partial differential equations. This method is restricted by a local CFL (Courant Friedrichs Lewy) condition rather than the traditional global CFL condition. Moreover, contrary to other local time-stepping (LTS) methods, the asynchronous algorithm permits the selection of independent time steps in each mesh element. We derived an asynchronous Runge–Kutta 2 (ARK2) scheme from a standard explicit Runge–Kutta method and we proved that the ARK2 scheme is second order convergent. Comparing with the classical integration, the asynchronous scheme is effective in terms of computation time.

      PubDate: 2017-07-23T13:02:58Z
      DOI: 10.1016/j.apnum.2017.06.014
      Issue No: Vol. 121 (2017)
       
  • A numerical method for solving some model problems arising in science and
           convergence analysis based on residual function
    • Authors: Ömür Kıvanç Kürkçü; Ersin Aslan; Mehmet Sezer
      Pages: 134 - 148
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): Ömür Kıvanç Kürkçü, Ersin Aslan, Mehmet Sezer
      In this study, we solve some widely-used model problems consisting of linear, nonlinear differential and integral equations, employing Dickson polynomials with the parameter-α and the collocation points for an efficient matrix method. The convergence of a Dickson polynomial solution of the model problem is investigated by means of the residual function. We encode useful computer programs for model problems, in order to obtain the precise Dickson polynomial solutions. These solutions are plotted along with the exact solutions in figures and the numerical results are compared with other well-known methods in tables.

      PubDate: 2017-07-23T13:02:58Z
      DOI: 10.1016/j.apnum.2017.06.015
      Issue No: Vol. 121 (2017)
       
  • An adaptive Galerkin method for the time-dependent complex
           Schrödinger equation
    • Authors: A.I. Ávila; A. Meister; M. Steigemann
      Pages: 149 - 169
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): A.I. Ávila, A. Meister, M. Steigemann
      Nonlinear time-dependent Schrödinger equations (NLSE) model several important problems in quantum physics and morphogenesis. Recently, vortex lattice formation were experimentally found in Bose–Einstein condensate and Fermi superfluids, which are modeled by adding a rotational term in the NLSE equation. Numerical solutions have been computed by using separate approaches for time and space variables. If we see the complex equation as a system, wave methods can be used. In this article, we consider finite element approximations using continuous Galerkin schemes in time and space by adaptive mesh balancing both errors. To get this balance, we adapt the dual weighted residual method used for wave equations and estimates of error indicators for adaptive space–time finite element discretization. The results show how important is dynamic refinement to control the degrees of freedom in space.

      PubDate: 2017-08-03T13:52:30Z
      DOI: 10.1016/j.apnum.2017.06.013
      Issue No: Vol. 121 (2017)
       
  • Nonsmooth data error estimates for FEM approximations of the time
           fractional cable equation
    • Authors: Peng Zhu; Shenglan Xie; Xiaoshen Wang
      Pages: 170 - 184
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): Peng Zhu, Shenglan Xie, Xiaoshen Wang
      In this paper, the fractional cable equation, involving two Riemann–Liouville fractional derivatives, with initial/boundary condition is considered. Two fully discrete schemes are obtained by employing piecewise linear Galerkin FEM in space, and using convolution quadrature methods based on the first- and second-order backward difference methods in time. Optimal error estimates in terms of the initial data and the inhomogeneity for the semi-discrete scheme and fully discrete schemes are discussed. Numerical results are shown to verify the theoretical results.

      PubDate: 2017-08-03T13:52:30Z
      DOI: 10.1016/j.apnum.2017.07.005
      Issue No: Vol. 121 (2017)
       
  • Fast and exact 2d image reconstruction based on Hakopian interpolation
    • Authors: Xuenan Sun; Xuezhang Liang
      Pages: 185 - 197
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): Xuenan Sun, Xuezhang Liang
      A new algorithm for the reconstruction of two-dimensional (2D) images from projections is given. The algorithm is based on the expansions of Hakopian interpolation polynomial into Chebyshev–Fourier series. The computer simulation experiments show that the new algorithm is effective.

      PubDate: 2017-08-03T13:52:30Z
      DOI: 10.1016/j.apnum.2017.07.002
      Issue No: Vol. 121 (2017)
       
  • Novel alternating update method for low rank approximation of structured
           matrices
    • Authors: Jianchao Bai; Jicheng Li; Pingfan Dai
      Pages: 223 - 233
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): Jianchao Bai, Jicheng Li, Pingfan Dai
      This work is devoted to designing a unified alternating update method for solving a class of structured low rank approximations under the convex and unitarily invariant norm. By the aid of the variational inequality and monotone operator, the proposed method is proved to converge to the solution point of an equivalent variational inequality with a worst-case O ( 1 / t ) convergence rate in a nonergodic sense. We also analyze that the involved subproblems under the Frobenius norm are respectively equivalent to the structured least-squares problem and low rank least-squares problem, where the explicit solutions to some special cases are derived. In order to investigate the efficiency of the proposed method, several examples in system identification are tested to validate that the proposed method can outperform some state-of-the-art methods.

      PubDate: 2017-08-03T13:52:30Z
      DOI: 10.1016/j.apnum.2017.07.001
      Issue No: Vol. 121 (2017)
       
  • Construction of IMEX DIMSIMs of high order and stage order
    • Authors: Z. Jackiewicz; H. Mittelmann
      Pages: 234 - 248
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): Z. Jackiewicz, H. Mittelmann
      For many systems of differential equations modeling problems in science and engineering, there are often natural splittings of the right hand side into two parts, one of which is non-stiff or mildly stiff, and the other part is stiff. Such systems can be efficiently treated by a class of implicit–explicit (IMEX) diagonally implicit multistage integration methods (DIMSIMs), where the stiff part is integrated by implicit formula, and the non-stiff part is integrated by an explicit formula. We analyze stability of these methods when the implicit and explicit parts interact with each other. We look for methods with large absolute stability region, assuming that the implicit part of the method is A ( α ) -, A-, or L-stable. Finally, we furnish examples of IMEX DIMSIMs of order p = 5 and p = 6 and stage order q = p , with good stability properties. Numerical examples illustrate that the IMEX schemes constructed in this paper do not suffer from order reduction phenomenon for some range of stepsizes.

      PubDate: 2017-08-03T13:52:30Z
      DOI: 10.1016/j.apnum.2017.07.004
      Issue No: Vol. 121 (2017)
       
  • An error estimate for an energy conserving spectral scheme approximating
           the dynamic elastica with free ends
    • Authors: Kazuho Ito
      Pages: 1 - 20
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Kazuho Ito
      An energy conserving spectral scheme is presented for approximating the smooth solution of the dynamic elastica with free ends. The spatial discretization of the elastica is done on the basis of Galerkin spectral methods with a Legendre grid. It is established that the scheme has the unique solution and enjoys a spectral accuracy with respect to the size of the spatial grid. Moreover, some results of a numerical simulation are given to verify that the implemented scheme preserves the discrete energy.

      PubDate: 2017-05-13T08:01:38Z
      DOI: 10.1016/j.apnum.2017.05.001
      Issue No: Vol. 120 (2017)
       
  • A note on Hermite multiwavelets with polynomial and exponential vanishing
           moments
    • Authors: Mariantonia Cotronei; Nada Sissouno
      Pages: 21 - 34
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Mariantonia Cotronei, Nada Sissouno
      The aim of the paper is to present Hermite-type multiwavelets, i.e. wavelets acting on vector data representing function values and consecutive derivatives, which satisfy the vanishing moment property with respect to elements in the space spanned by exponentials and polynomials. Such functions satisfy a two-scale relation which is level-dependent as well as the corresponding multiresolution analysis. An important feature of the associated filters is the possibility of factorizing their symbols in terms of the so-called cancellation operator. This is shown, in particular, in the situation where Hermite multiwavelets are obtained by completing interpolatory level-dependent Hermite subdivision operators, reproducing polynomial and exponential data, to biorthogonal systems. A few constructions of families of multiwavelet filters of this kind are proposed.

      PubDate: 2017-05-22T13:25:42Z
      DOI: 10.1016/j.apnum.2017.04.009
      Issue No: Vol. 120 (2017)
       
  • First order system least squares pseudo-spectral method for
           Stokes–Darcy equations
    • Authors: Peyman Hessari; Byeong-Chun Shin
      Pages: 35 - 52
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Peyman Hessari, Byeong-Chun Shin
      The subject of this paper is to investigate the first order system least squares Legendre and Chebyshev pseudo-spectral methods for coupled Stokes–Darcy equations. By introducing strain tensor as a new variable, Stokes–Darcy equations recast into a system of first order differential equations. The least squares functional is defined by summing up the weighted L 2 -norm of residuals of the first order system for coupled Stokes–Darcy equations. To treat Beavers–Joseph–Saffman interface conditions, the weighted L 2 -norm of these conditions are also added to the least squares functional. Continuous and discrete homogeneous functionals are shown to be equivalent to the combination of weighted H ( div ) and H 1 -norm for Stokes–Darcy equations. The spectral convergence for the Legendre and Chebyshev methods are derived. To demonstrate this analysis, numerical experiments are also presented.

      PubDate: 2017-05-22T13:25:42Z
      DOI: 10.1016/j.apnum.2017.04.010
      Issue No: Vol. 120 (2017)
       
  • Error analysis of a compact finite difference method for fourth-order
           nonlinear elliptic boundary value problems
    • Authors: Yuan-Ming Wang
      Pages: 53 - 67
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Yuan-Ming Wang
      This paper is concerned with a compact finite difference method with non-isotropic mesh sizes for a two-dimensional fourth-order nonlinear elliptic boundary value problem. By the discrete energy analysis, the optimal error estimates in the discrete L 2 , H 1 and L ∞ norms are obtained without any constraint on the mesh sizes. The error estimates show that the compact finite difference method converges with the convergence rate of fourth-order. Based on a high-order approximation of the solution, a Richardson extrapolation algorithm is developed to make the final computed solution sixth-order accurate. Numerical results demonstrate the high-order accuracy of the compact finite difference method and its extrapolation algorithm in the discrete L 2 , H 1 and L ∞ norms.

      PubDate: 2017-05-22T13:25:42Z
      DOI: 10.1016/j.apnum.2017.04.011
      Issue No: Vol. 120 (2017)
       
  • Optimal error estimate of a compact scheme for nonlinear Schrödinger
           equation
    • Authors: Jialin Hong; Lihai Ji; Linghua Kong; Tingchun Wang
      Pages: 68 - 81
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Jialin Hong, Lihai Ji, Linghua Kong, Tingchun Wang
      It has been pointed out in literature that the symplectic scheme of a nonlinear Hamiltonian system can not preserve the total energy in the discrete sense Ge and Marsden (1988) [10]. Moreover, due to the difficulty in obtaining a priori estimate of the numerical solution, it is very hard to establish the optimal error bound of the symplectic scheme without any restrictions on the grid ratios. In this paper, we develop and analyze a compact scheme for solving nonlinear Schrödinger equation. We introduce a cut-off technique for proving optimal L ∞ error estimate for the compact scheme. We show that the convergence of the compact scheme is of second order in time and of fourth order in space. Meanwhile, we define a new type of energy functional by using a recursion relationship, and then prove that the compact scheme is mass and energy-conserved, symplectic-conserved, unconditionally stable and can be computed efficiently. Numerical experiments confirm well the theoretical analysis results.

      PubDate: 2017-05-22T13:25:42Z
      DOI: 10.1016/j.apnum.2017.05.004
      Issue No: Vol. 120 (2017)
       
  • A smoothing Newton method for absolute value equation associated with
           second-order cone
    • Authors: Xin-He Miao; Jian-Tao Yang; B. Saheya; Jein-Shan Chen
      Pages: 82 - 96
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Xin-He Miao, Jian-Tao Yang, B. Saheya, Jein-Shan Chen
      In this paper, we consider the smoothing Newton method for solving a type of absolute value equations associated with second order cone (SOCAVE for short), which is a generalization of the standard absolute value equation frequently discussed in the literature during the past decade. Based on a class of smoothing functions, we reformulate the SOCAVE as a family of parameterized smooth equations, and propose the smoothing Newton algorithm to solve the problem iteratively. Moreover, the algorithm is proved to be locally quadratically convergent under suitable conditions. Preliminary numerical results demonstrate that the algorithm is effective. In addition, two kinds of numerical comparisons are presented which provides numerical evidence about why the smoothing Newton method is employed and also suggests a suitable smoothing function for future numerical implementations. Finally, we point out that although the main idea for proving the convergence is similar to the one used in the literature, the analysis is indeed more subtle and involves more techniques due to the feature of second-order cone.

      PubDate: 2017-05-22T13:25:42Z
      DOI: 10.1016/j.apnum.2017.04.012
      Issue No: Vol. 120 (2017)
       
  • Two-step algorithms for the stationary incompressible Navier–Stokes
           equations with friction boundary conditions
    • Authors: Hailong Qiu; Rong An; Liquan Mei; Changfeng Xue
      Pages: 97 - 114
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Hailong Qiu, Rong An, Liquan Mei, Changfeng Xue
      Two-step algorithms for the stationary incompressible Navier–Stokes equations with friction boundary conditions are considered in this paper. Our algorithms consist of solving one Navier–Stokes variational inequality problem used the linear equal-order finite element pair (i.e., P 1 – P 1 ) and then solving a linearization variational inequality problem used the quadratic equal-order finite element pair (i.e., P 2 – P 2 ). Moreover, the stability and convergence of our two-step algorithms are derived. Finally, numerical tests are presented to check theoretical results.

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.05.003
      Issue No: Vol. 120 (2017)
       
  • Truncated transparent boundary conditions for second order hyperbolic
           systems
    • Authors: Ivan Sofronov
      Pages: 115 - 124
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Ivan Sofronov
      In [22] we announced equations for yielding differential operators of transparent boundary conditions (TBCs) for a certain class of second order hyperbolic systems. Here we present the full derivation of these equations and consider ways of their solving. The solutions represent local parts of TBCs, and they can be used as approximate nonreflecting boundary conditions. We give examples of computing such conditions called ‘truncated TBCs’ for 3D elasticity and Biot poroelasticity

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.05.002
      Issue No: Vol. 120 (2017)
       
  • Second order approximations for kinetic and potential energies in
           Maxwell's wave equations
    • Authors: J.A. Ferreira; D. Jordão; L. Pinto
      Pages: 125 - 140
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): J.A. Ferreira, D. Jordão, L. Pinto
      In this paper we propose a numerical scheme for wave type equations with damping and space variable coefficients. Relevant equations of this kind arise for instance in the context of Maxwell's equations, namely, the electric potential equation and the electric field equation. The main motivation to study such class of equations is the crucial role played by the electric potential or the electric field in enhanced drug delivery applications. Our numerical method is based on piecewise linear finite element approximation and it can be regarded as a finite difference method based on non-uniform partitions of the spatial domain. We show that the proposed method leads to second order convergence, in time and space, for the kinetic and potential energies with respect to a discrete L 2 -norm.

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.05.005
      Issue No: Vol. 120 (2017)
       
  • A mixed finite element approximation for Darcy–Forchheimer flows of
           slightly compressible fluids
    • Authors: Thinh Kieu
      Pages: 141 - 164
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Thinh Kieu
      In this paper, we consider the generalized Forchheimer flows for slightly compressible fluids in porous media. Using Muskat's and Ward's general form of Forchheimer equations, we describe the flow of a single-phase fluid in R d , d ≥ 2 by a nonlinear degenerate system of density and momentum. A mixed finite element method is proposed for the approximation of the solution of the above system. The stability of the approximations are proved; the error estimates are derived for the numerical approximations for both continuous and discrete time procedures. The continuous dependence of numerical solutions on physical parameters are demonstrated. Experimental studies are presented regarding convergence rates and showing the dependence of the solution on the physical parameters.

      PubDate: 2017-06-06T14:38:08Z
      DOI: 10.1016/j.apnum.2017.05.006
      Issue No: Vol. 120 (2017)
       
  • Starting procedures for general linear methods
    • Authors: G. Califano; G. Izzo; Z. Jackiewicz
      Pages: 165 - 175
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): G. Califano, G. Izzo, Z. Jackiewicz
      We present a systematic approach to the construction of starting procedures for general linear methods (GLMs) of order p and stage order q = p . Order conditions for starting procedures based on the generalized Runge–Kutta (RK) are derived using the theory of rooted trees, elementary differentials, and elementary weights, and examples of generalized RK formulas are given up to the order p = 4 .

      PubDate: 2017-07-23T13:02:58Z
      DOI: 10.1016/j.apnum.2017.05.009
      Issue No: Vol. 120 (2017)
       
  • Single measurement experimental data for an inverse medium problem
           inverted by a multi-frequency globally convergent numerical method
    • Authors: Aleksandr E. Kolesov; Michael V. Klibanov; Loc H. Nguyen; Dinh-Liem Nguyen; Nguyen T. Thành
      Pages: 176 - 196
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Aleksandr E. Kolesov, Michael V. Klibanov, Loc H. Nguyen, Dinh-Liem Nguyen, Nguyen T. Thành
      The recently developed globally convergent numerical method for an inverse medium problem with the data resulting from a single measurement, proposed in [23], is tested on experimental data. The data were originally collected in the time domain, whereas the method works in the frequency domain with the multi-frequency data. Due to a significant amount of noise in the measured data, a straightforward application of the Fourier transform to these data does not work. Hence, we develop a heuristic data preprocessing procedure, which is described in the paper. The preprocessed data are used as the input for the inversion algorithm. Numerical results demonstrate a good accuracy of the reconstruction of both refractive indices and locations of targets.

      PubDate: 2017-06-06T14:38:08Z
      DOI: 10.1016/j.apnum.2017.05.007
      Issue No: Vol. 120 (2017)
       
  • Stability and error analysis of the reproducing kernel Hilbert space
           method for the solution of weakly singular Volterra integral equation on
           graded mesh
    • Authors: Hossein Beyrami; Taher Lotfi; Katayoun Mahdiani
      Pages: 197 - 214
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Hossein Beyrami, Taher Lotfi, Katayoun Mahdiani
      In this article, we approximate the solution of the weakly singular Volterra integral equation of the second kind using the reproducing kernel Hilbert space (RKHS) method. This method does not require any background mesh and can easily be implemented. Since the solution of the second kind weakly singular Volterra integral equation has unbounded derivative at the left end point of the interval of the integral equation domain, RKHS method has poor convergence rate on the conventional uniform mesh. Consequently, the graded mesh is proposed. Using error analysis, we show the RKHS method has better convergence rate on the graded mesh than the uniform mesh. Numerical examples are given to confirm the error analysis results. Regularization of the solution is an alternative approach to improve the efficiency of the RKHS method. In this regard, an smooth transformation is used to regularization and obtained numerical results are compared with other methods.

      PubDate: 2017-06-12T13:07:08Z
      DOI: 10.1016/j.apnum.2017.05.010
      Issue No: Vol. 120 (2017)
       
  • Strong convergence of the split-step theta method for neutral stochastic
           delay differential equations
    • Authors: Zhiping Yan; Aiguo Xiao; Xiao Tang
      Pages: 215 - 232
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Zhiping Yan, Aiguo Xiao, Xiao Tang
      Neutral stochastic delay differential equations often appear in various fields of science and engineering. The aim of this article is to investigate the strong convergence of the split-step theta (SST) method for the neutral stochastic delay differential equations, where the corresponding coefficients may be highly nonlinear with respect to the delay variables. In particular, we reveal that the SST method with θ ∈ [ 0 , 1 ] strongly converges to the exact solution with the order 1 2 . Some numerical results are presented to confirm the obtained results.

      PubDate: 2017-06-12T13:07:08Z
      DOI: 10.1016/j.apnum.2017.05.008
      Issue No: Vol. 120 (2017)
       
  • Exponentially graded mesh for a singularly perturbed problem with two
           small parameters
    • Authors: Helena Zarin
      Pages: 233 - 242
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Helena Zarin
      A one-dimensional singularly perturbed boundary value problem with two small perturbation parameters is numerically solved on an exponentially graded mesh. Using an h-version of the standard Galerkin method with higher order polynomials, we prove a robust convergence in the corresponding energy norm. Numerical experiments support theoretical findings.

      PubDate: 2017-06-21T15:41:03Z
      DOI: 10.1016/j.apnum.2017.06.003
      Issue No: Vol. 120 (2017)
       
  • A fully discrete pseudospectral method for Fisher's equation on the whole
           line
    • Authors: Tian-jun Wang; Yu-jian Jiao
      Pages: 243 - 256
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Tian-jun Wang, Yu-jian Jiao
      In this paper, a fully discrete pseudospectral scheme for Fisher's equation whose solutions behave differently as x → + ∞ and x → − ∞ is presented using generalized Hermite interpolation. The convergence and the stability of the proposed scheme are analyzed. Numerical results coincide well with theoretical analysis and show efficiency of our algorithm.

      PubDate: 2017-07-02T16:25:43Z
      DOI: 10.1016/j.apnum.2017.06.002
      Issue No: Vol. 120 (2017)
       
  • Convergence and dynamics of structurally identical root finding methods
    • Authors: Mário Basto; Teresa Abreu; Viriato Semiao; Francisco L. Calheiros
      Pages: 257 - 269
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Mário Basto, Teresa Abreu, Viriato Semiao, Francisco L. Calheiros
      The behavior of an iterative method applied to nonlinear equations may be considerably sensitive to the starting points. Comparisons between iterative methods are supported by the study of the basins of attraction in the complex plane C . However, usually, nothing is said about the rate of convergence. In this paper, by making recourse to several examples of algebraic and transcendental equations, a numerical comparison is performed between three methods with the same structure, namely BSC, Halley's and Euler–Chebyshev's methods. The study takes into account both the basins of attraction and the rate of convergence which is measured as the number of iterations required to obtain an equation root with a given tolerance.

      PubDate: 2017-07-02T16:25:43Z
      DOI: 10.1016/j.apnum.2017.06.006
      Issue No: Vol. 120 (2017)
       
  • Finite element method for a symmetric tempered fractional diffusion
           equation
    • Authors: Cem Çelik; Melda Duman
      Pages: 270 - 286
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Cem Çelik, Melda Duman
      A space fractional diffusion equation involving symmetric tempered fractional derivative of order 1 < α < 2 is considered. A Galerkin finite element method is implemented to obtain spatial semi-discrete scheme and first order centered difference in time is used to find a fully discrete scheme for tempered fractional diffusion equation. We construct a variational formulation and show its existence, uniqueness and regularity. Stability and error estimates of numerical scheme are discussed. The theoretical and computational study of accuracy and consistence of the numerical solutions are presented.

      PubDate: 2017-07-02T16:25:43Z
      DOI: 10.1016/j.apnum.2017.05.012
      Issue No: Vol. 120 (2017)
       
  • Stabilized Lagrange multiplier method for elliptic and parabolic interface
           problems
    • Authors: Ajit Patel; Sanjib Kumar Acharya; Amiya Kumar Pani
      Pages: 287 - 304
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): Ajit Patel, Sanjib Kumar Acharya, Amiya Kumar Pani
      In this paper, we discuss a new stabilized Lagrange multiplier method for finite element solution of multi-domain elliptic and parabolic initial-boundary value problems with non-matching grid across the subdomain interfaces. The proposed method is consistent with the original problem and its stability is established without using the inf-sup (well known as LBB) condition. In the first part of this article, optimal error estimates are derived for second order elliptic interface problems. Then, the analysis is extended to parabolic initial and boundary value problems with interface and optimal error estimates are established for both semi-discrete and completely discrete schemes. The results of numerical experiments support the theoretical results obtained in this article.

      PubDate: 2017-07-02T16:25:43Z
      DOI: 10.1016/j.apnum.2017.05.011
      Issue No: Vol. 120 (2017)
       
  • Identification of a memory kernel in a nonlinear integrodifferential
           parabolic problem
    • Authors: K. Van Bockstal; M. Slodička; F. Gistelinck
      Pages: 305 - 323
      Abstract: Publication date: October 2017
      Source:Applied Numerical Mathematics, Volume 120
      Author(s): K. Van Bockstal, M. Slodička, F. Gistelinck
      In this contribution, the reconstruction of a solely time-dependent convolution kernel in an nonlinear parabolic equation is studied. The missing kernel is recovered from a global integral measurement. The existence, uniqueness and regularity of a weak solution is addressed. More specific, a numerical algorithm based on Rothe's method is designed. Numerical experiments support the obtained results.

      PubDate: 2017-07-02T16:25:43Z
      DOI: 10.1016/j.apnum.2017.06.004
      Issue No: Vol. 120 (2017)
       
  • Unconditional error estimates for time dependent viscoelastic fluid flow
    • Authors: Haibiao Zheng; Jiaping Yu; Li Shan
      Pages: 1 - 17
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Haibiao Zheng, Jiaping Yu, Li Shan
      The unconditional convergence of finite element method for two-dimensional time-dependent viscoelastic flow with an Oldroyd B constitutive equation is given in this paper, while all previous works require certain time-step restrictions. The approximation is stabilized by using the Discontinuous Galerkin (DG) approximation for the constitutive equation. The analysis bases on a splitting of the error into two parts: the error from the time discretization of the PDEs and the error from the finite element approximation of corresponding iterated time-discrete PDEs. The approach used in this paper can be applied to more general couple nonlinear parabolic and hyperbolic systems.

      PubDate: 2017-04-04T17:32:23Z
      DOI: 10.1016/j.apnum.2017.03.010
      Issue No: Vol. 119 (2017)
       
  • A numerical method for solving the time variable fractional order
           mobile–immobile advection–dispersion model
    • Authors: Wei Jiang; Na Liu
      Pages: 18 - 32
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Wei Jiang, Na Liu
      In this article, we proposed a new numerical method to obtain the approximation solution for the time variable fractional order mobile–immobile advection–dispersion model based on reproducing kernel theory and collocation method. The equation is obtained from the standard advection–dispersion equation (ADE) by adding the Coimbra's variable fractional derivative in time of order γ ( x , t ) ∈ [ 0 , 1 ] . In order to solve this kind of equation, we discuss and derive the ε-approximate solution in the form of series with easily computable terms in the bivariate spline space. At the same time, the stability and convergence of the approximation are investigated. Finally, numerical examples are provided to show the accuracy and effectiveness.

      PubDate: 2017-04-11T18:11:42Z
      DOI: 10.1016/j.apnum.2017.03.014
      Issue No: Vol. 119 (2017)
       
  • Difference schemes for systems of second order nonlinear ODEs on a
           semi-infinite interval
    • Authors: M. Król; M.V. Kutniv; O.I. Pazdriy
      Pages: 33 - 50
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): M. Król, M.V. Kutniv, O.I. Pazdriy
      The three-point difference schemes of high order accuracy for the numerical solving boundary value problems on a semi-infinite interval for systems of second order nonlinear ordinary differential equations with a not self-conjugate operator are constructed and justified. We proved the existence and uniqueness of solutions of the three-point difference schemes and obtained the estimate of their accuracy. The results of numerical experiments which confirm the theoretical results are given.

      PubDate: 2017-04-11T18:11:42Z
      DOI: 10.1016/j.apnum.2017.03.012
      Issue No: Vol. 119 (2017)
       
  • Spectral element technique for nonlinear fractional evolution equation,
           stability and convergence analysis
    • Authors: Mehdi Dehghan; Mostafa Abbaszadeh
      Pages: 51 - 66
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Mehdi Dehghan, Mostafa Abbaszadeh
      In the current manuscript, we consider a fractional partial integro-differential equation that is called fractional evolution equation. The fractional evolution equation is based on the Riemann–Liouville fractional integral. The presented numerical algorithm is based on the following procedures: at first a difference scheme has been used to discrete the temporal direction and secondly the spectral element method is applied to discrete the spatial direction and finally these procedures are combined to obtain a full-discrete scheme. For the constructed numerical technique, we prove the unconditional stability and also obtain an error bound. We use the energy method to analysis the full-discrete scheme. We employ some test problems to show the high accuracy of the proposed technique. Also, we compare the obtained numerical results using the present method with the existing methods in the literature.

      PubDate: 2017-04-19T19:09:14Z
      DOI: 10.1016/j.apnum.2017.03.009
      Issue No: Vol. 119 (2017)
       
  • Second order time relaxation model for accelerating convergence to
           steady-state equilibrium for Navier–Stokes equations
    • Authors: Osman Rasit Isik; Aziz Takhirov; Haibiao Zheng
      Pages: 67 - 78
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Osman Rasit Isik, Aziz Takhirov, Haibiao Zheng
      This paper deals with the problem of accelerating convergence to equilibrium for the Navier–Stokes equation using time relaxation models. We show that the BDF2 based semidiscrete solution of the regularized scheme converges to the steady-state solution of the continuous Navier–Stokes equations, under appropriate conditions. The proof also shows that time relaxation model can be used to accelerate the convergence with the appropriate choice of the parameters. Numerical experiment is presented to illustrate the theory.

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.03.016
      Issue No: Vol. 119 (2017)
       
  • A new approach to the construction of DIMSIMs of high order and stage
           order
    • Authors: I.Th. Famelis; Z. Jackiewicz
      Pages: 79 - 93
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): I.Th. Famelis, Z. Jackiewicz
      In this work we describe a new approach to the construction of diagonally implicit multistage integration methods (DIMSIMs) for the numerical solution of initial value problems for ordinary differential equations (ODEs). Differential Evolution, a very popular computational intelligence technique is employed to construct type 1 and type 2 methods with better or equivalent characteristics to the methods presented in the literature. The numerical results in selected problems justify this argument.

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.03.015
      Issue No: Vol. 119 (2017)
       
  • Order reduction phenomenon for general linear methods
    • Authors: Michał Braś; Angelamaria Cardone; Zdzisław Jackiewicz; Bruno Welfert
      Pages: 94 - 114
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Michał Braś, Angelamaria Cardone, Zdzisław Jackiewicz, Bruno Welfert
      The order reduction phenomenon for general linear methods (GLMs) for stiff differential equations is investigated. It turns out that, similarly as for standard Runge–Kutta methods, the effective order of convergence for a large class of GLMs applied to stiff differential systems, is equal to the stage order of the method. In particular, it is demonstrated that the global error ‖ e [ n ] ‖ of GLMs of order p and stage order q applied to the Prothero–Robinson test problem y ′ ( t ) = λ ( y ( t ) − φ ( t ) ) + φ ′ ( t ) , t ∈ [ t 0 , T ] , y ( t 0 ) = φ ( t 0 ) , is O ( h q ) + O ( h p ) as h → 0 and h λ → − ∞ . Moreover, for GLMs with Runge–Kutta stability which are A ( 0 ) -stable and for which the stability function R ( z ) of the underlying Runge–Kutta methods, (i.e., the corresponding RK methods which have the same absolute stability properties as the GLMs), is such that R ( ∞ ) ≠ 1 , the global error satisfies ‖ e [ n ] ‖ = O ( h q + 1 ) + O ( h p ) as h → 0 and h λ → − ∞ . These results are confirmed by numerical experiments.

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.04.001
      Issue No: Vol. 119 (2017)
       
  • A meshless scheme for Hamiltonian partial differential equations with
           conservation properties
    • Authors: Zhengjie Sun; Wenwu Gao
      Pages: 115 - 125
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Zhengjie Sun, Wenwu Gao
      Based on quasi-interpolation, the paper proposes a meshless scheme for Hamiltonian PDEs with conservation properties. There are two key features of the proposed scheme. First, it is constructed from scattered sampling data. Second, it conserves energy for both linear and nonlinear Hamiltonian PDEs. Moreover, if the considered Hamiltonian PDEs additionally possess some other quadric invariants (i.e., the mass in the Schrödinger equation), then it can even preserve them. Error estimates (including the truncation error and the global error) of the scheme are also derived in the paper. To demonstrate the efficiency and superiority of the scheme, some numerical examples are provided at the end of the paper. Both theoretical and numerical results demonstrate that the scheme is simple, easy to compute, efficient and stable. More importantly, the scheme conserves the discrete energy and thus captures the long-time dynamics of Hamiltonian systems.

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.04.005
      Issue No: Vol. 119 (2017)
       
  • Neumann problems of 2D Laplace's equation by method of fundamental
           solutions
    • Authors: Zi-Cai Li; Ming-Gong Lee; Hung-Tsai Huang; John Y. Chiang
      Pages: 126 - 145
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Zi-Cai Li, Ming-Gong Lee, Hung-Tsai Huang, John Y. Chiang
      The method of fundamental solutions (MFS) was first used by Kupradze in 1963 [21]. Since then, there have appeared numerous reports of the MFS. Most of the existing analysis for the MFS are confined to Dirichlet problems on disk domains. It seems to exist no analysis for Neumann problems. This paper is devoted to Neumann problems in non-disk domains, and the new stability analysis and the error analysis are made. The bounds for both condition numbers and errors are derived in detail. The optimal convergence rates in L 2 and H 1 norms in S are achieved, and the condition number grows exponentially as the number of fundamental functions increases. To reduce the huge condition numbers, the truncated singular value decomposition (TSVD) may be solicited. Numerical experiments are provided to support the analysis made. The analysis for Neumann problems in this paper is intriguing due to its distinct features.

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.04.004
      Issue No: Vol. 119 (2017)
       
  • A fast solution technique for finite element discretization of the
           space–time fractional diffusion equation
    • Authors: Zhengguang Liu; Aijie Cheng; Xiaoli Li; Hong Wang
      Pages: 146 - 163
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Zhengguang Liu, Aijie Cheng, Xiaoli Li, Hong Wang
      In this paper, we study fast Galerkin finite element methods to solve a space–time fractional diffusion equation. We develop an optimal piecewise-linear and piecewise-quadratic finite element methods for solving this problem and give optimal error estimates. Furthermore, we develop piecewise-constant discontinuous finite element method for discontinuous problem of this model. Importantly, a fast solution technique to accelerate non-square Toeplitz matrix–vector multiplications which arise from both continuous and discontinuous Galerkin finite element discretization respectively is considered. This fast solution technique is based on fast Fourier transform and depends on the special structure of coefficient matrices and it helps to reduce the computational work from O ( N 3 ) required by the traditional methods to O ( N log 2 ⁡ N ) , where N is the size (number of spatial grid points) of the coefficient matrices for every time step. Moreover, the applicability and accuracy of the method are demonstrated by numerical experiments to support our theoretical analysis.

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.04.003
      Issue No: Vol. 119 (2017)
       
  • Efficient implementation of RKN-type Fourier collocation methods for
           second-order differential equations
    • Authors: Bin Wang; Fanwei Meng; Yonglei Fang
      Pages: 164 - 178
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Bin Wang, Fanwei Meng, Yonglei Fang
      In this paper we discuss the efficient implementation of RKN-type Fourier collocation methods, which are used when solving second-order differential equations. The proposed implementation relies on an alternative formulation of the methods and their blended formulation. The features and effectiveness of the implementation are confirmed by the performance of the methods on three numerical tests.

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.04.008
      Issue No: Vol. 119 (2017)
       
  • A second order operator splitting numerical scheme for the
           “good” Boussinesq equation
    • Authors: Cheng Zhang; Hui Wang; Jingfang Huang; Cheng Wang; Xingye Yue
      Pages: 179 - 193
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Cheng Zhang, Hui Wang, Jingfang Huang, Cheng Wang, Xingye Yue
      The nonlinear stability and convergence analyses are presented for a second order operator splitting scheme applied to the “good” Boussinesq equation, coupled with the Fourier pseudo-spectral approximation in space. Due to the wave equation nature of the model, we have to rewrite it as a system of two equations, for the original variable u and v = u t , respectively. In turn, the second order operator splitting method could be efficiently designed. A careful Taylor expansion indicates the second order truncation error of such a splitting approximation, and a linearized stability analysis for the numerical error function yields the desired convergence estimate in the energy norm. In more details, the convergence in the energy norm leads to an ℓ ∞ ( 0 , T ⁎ ; H 2 ) convergence for the numerical solution u and ℓ ∞ ( 0 , T ⁎ ; ℓ 2 ) convergence for v = u t . And also, the presented convergence is unconditional for the time step in terms of the spatial grid size, in comparison with a severe time step restriction, Δ t ≤ C h 2 , required in many existing works.

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.04.006
      Issue No: Vol. 119 (2017)
       
  • Numerical analysis of cubic orthogonal spline collocation methods for the
           coupled Schrödinger–Boussinesq equations
    • Authors: Feng Liao; Luming Zhang; Shanshan Wang
      Pages: 194 - 212
      Abstract: Publication date: September 2017
      Source:Applied Numerical Mathematics, Volume 119
      Author(s): Feng Liao, Luming Zhang, Shanshan Wang
      In this article, we formulate two orthogonal spline collocation schemes, which consist of a nonlinear and a linear scheme for solving the coupled Schrödinger–Boussinesq equations numerically. Firstly, the conservation laws of our schemes are derived. Secondly, the existence solutions of our schemes are investigated. Thirdly, the convergence and stability of the nonlinear scheme are analyzed by means of discrete energy methods, while the convergence of the linear scheme is proved by cut-off function technique. Finally, numerical results are reported to verify our theoretical analysis for the numerical methods.

      PubDate: 2017-06-02T14:30:28Z
      DOI: 10.1016/j.apnum.2017.04.007
      Issue No: Vol. 119 (2017)
       
  • Convergence and stability analysis of heterogeneous time step coupling
           schemes for parabolic problems
    • Authors: Michal
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): Michal Beneš
      We propose and rigorously analyze the subcycling method based on primal domain decomposition techniques for first-order transient partial differential equations. In time dependent problems, it can be computationally advantageous to use different time steps in different regions. Smaller time steps are used in regions of significant changes in the solution and larger time steps are prescribed in regions with nearly stationary response. Subcycling can efficiently reduce the total computational cost. Crucial to our approach is a nonstandard heterogeneous temporal discretization. We begin with the discretization in time by the asynchronous Rothe method, which, in essence, involves a backward finite difference scheme assuming different time steps (fine and large time steps) in different parts of the computational domain. The emphasis of the paper is on qualitative properties of the new numerical scheme, such as a-priori estimates, existence of the time-discrete solutions and the strong convergence and stability analysis. Several numerical experiments were conducted to examine the consistency of the proposed method.

      PubDate: 2017-08-03T13:52:30Z
       
  • Numerical analysis of an operational Jacobi Tau method for fractional
           weakly singular integro-differential equations
    • Authors: Mokhtary
      Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): P. Mokhtary
      The main concern of this paper is to develop and analyze an operational Tau method for obtaining the numerical solution of fractional weakly singular integro-differential equations when the Jacobi polynomials are used as natural basis functions. This strategy is an application of the matrix–vector–product approach in Tau formulation of the problem. We first study the regularity of the exact solution and show that some derivatives of the exact solution have a singularity at origin dependence on both order of fractional derivative and weakly singular kernel function which makes poor convergence results for the Tau discretization of the problem. In order to recover high-order of convergence, we propose a new variable transformation to regularize the given functions and then to approximate the solution via a satisfactory order of convergence using an operational Tau method. Convergence analysis of this novel method is presented and the expected spectral rate of convergence for the proposed method is established. Numerical results are given which confirm both the theoretical predictions obtained and efficiency of the proposed method.

      PubDate: 2017-07-12T12:47:24Z
       
  • Recognition of a time-dependent source in a time-fractional wave equation
    • Abstract: Publication date: November 2017
      Source:Applied Numerical Mathematics, Volume 121
      Author(s): K. Šišková, M. Slodička
      In the present paper, we deal with an inverse source problem for a time-fractional wave equation in a bounded domain in R d . The time-dependent source is determined from an additional measurement in the form of integral over the space subdomain. The existence, uniqueness and regularity of a weak solution are obtained. A numerical algorithm based on Rothe's method is proposed, a priori estimates are proved and convergence of iterates towards the solution is established.

      PubDate: 2017-07-02T16:25:43Z
       
 
 
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