Numerical solution for a general class of nonlocal nonlinear wave equations
Numerical Analysis
2015-09-03 v2
Abstract
A class of nonlocal nonlinear wave equation arises from the modeling of a one dimensional motion in a nonlinearly, nonlocally elastic medium. The equation involves a kernel function with nonnegative Fourier transform. We discretize the equation by using Fourier spectral method in space and we prove the convergence of the semidiscrete scheme. We then use a fully-discrete scheme, that couples Fourier pseudo-spectral method in space and 4th order Runge-Kutta in time, to observe the effect of the kernel function on solutions. To generate solitary wave solutions numerically, we use the Petviashvili's iteration method.
Cite
@article{arxiv.1507.08410,
title = {Numerical solution for a general class of nonlocal nonlinear wave equations},
author = {Handan Borluk and Gulcin M. Muslu},
journal= {arXiv preprint arXiv:1507.08410},
year = {2015}
}