Numerical approximation of solitary waves of the Benjamin equation
| Autor: | Dimitrios Mitsotakis, Vassilios A. Dougalis, Angel Durán |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Numerical Analysis
General Computer Science Discretization Applied Mathematics Mathematical analysis 01 natural sciences 010305 fluids & plasmas Theoretical Computer Science 010101 applied mathematics Nonlinear system symbols.namesake Fourier transform Numerical continuation Modeling and Simulation Conjugate gradient method 0103 physical sciences symbols 0101 mathematics Spectral method Focus (optics) Newton's method Mathematics |
| Zdroj: | Mathematics and Computers in Simulation. 127:56-79 |
| ISSN: | 0378-4754 |
| DOI: | 10.1016/j.matcom.2012.07.008 |
| Popis: | This paper presents several numerical techniques to generate solitary-wave profiles of the Benjamin equation. The formulation and implementation of the methods focus on some specific points of the problem: on the one hand, the approximation of the nonlocal term is accomplished by Fourier techniques, which determine the spatial discretization used in the experiments. On the other hand, in the numerical continuation procedure suggested by the derivation of the model and already discussed in the literature, several algorithms for solving the nonlinear systems are described and implemented: the Petviashvili method, the Preconditioned Conjugate Gradient Newton method and two Squared-Operator methods. A comparative study of these algorithms is made in the case of the Benjamin equation; Newton's method combined with Preconditioned Conjugate Gradient techniques, emerges as the most efficient. The resulting numerical profiles are shown to have a high accuracy as travelling-wave solutions when they are used as initial conditions in a time-stepping procedure for the Benjamin equation. The paper also explores the generation of multi-pulse solitary waves. |
| Databáze: | OpenAIRE |
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