Splitting methods for the nonlocal Fowler equation
| Autor: | Rémi Carles, Afaf Bouharguane |
|---|---|
| Přispěvatelé: | Equations aux Dérivées Partielles (EDP), Laboratoire Jean Kuntzmann (LJK), Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS)-Université Pierre Mendès France - Grenoble 2 (UPMF)-Université Joseph Fourier - Grenoble 1 (UJF)-Institut polytechnique de Grenoble - Grenoble Institute of Technology (Grenoble INP )-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques et de Modélisation de Montpellier (I3M), Centre National de la Recherche Scientifique (CNRS)-Université Montpellier 2 - Sciences et Techniques (UM2)-Université de Montpellier (UM), ANR-08-BLAN-0301,MathOcean,Analyse mathématique en océanographie et applications(2008) |
| Rok vydání: | 2013 |
| Předmět: |
Discrete-time Fourier transform
Numerical time integration 010103 numerical & computational mathematics 01 natural sciences symbols.namesake FOS: Mathematics Mathematics - Numerical Analysis Nonlocal operator Operator splitting Pseudo-spectral method 65M15 35K59 86A05 0101 mathematics Mathematics Fourier transform on finite groups Algebra and Number Theory Applied Mathematics Mathematical analysis Fourier inversion theorem Finite difference method Numerical Analysis (math.NA) 010101 applied mathematics Split-step method Split-step Fourier method Computational Mathematics Fourier transform Error analysis Fourier analysis symbols Stability [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] |
| Zdroj: | Mathematics of Computation Mathematics of Computation, American Mathematical Society, 2014, 83 (287), pp.1121-1141. ⟨10.1090/S0025-5718-2013-02757-3⟩ |
| ISSN: | 1088-6842 0025-5718 |
| DOI: | 10.1090/s0025-5718-2013-02757-3 |
| Popis: | We consider a nonlocal scalar conservation law proposed by Andrew C. Fowler to describe the dynamics of dunes, and we develop a numerical procedure based on splitting methods to approximate its solutions. We begin by proving the convergence of the well-known Lie formula, which is an approximation of the exact solution of order one in time. We next use the split-step Fourier method to approximate the continuous problem using the fast Fourier transform and the finite difference method. Our numerical experiments confirm the theoretical results. Comment: 20 pages, 3 figures. Presentation modified, some errors fixed |
| Databáze: | OpenAIRE |
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