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arXiv · 1507.08410

Numerical solution for a general class of nonlocal nonlinear wave equations

Handan Borluk·Gulcin M. Muslu
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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.

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Handan Borluk, Gulcin M. Muslu. 2015-07-30. Numerical solution for a general class of nonlocal nonlinear wave equations. https://arxiv.org/abs/1507.08410

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