Numerical solution for a general class of nonlocal nonlinear wave equations arising in elasticity


Muslu G. M. , BORLUK H.

ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, vol.97, no.12, pp.1600-1610, 2017 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 97 Issue: 12
  • Publication Date: 2017
  • Doi Number: 10.1002/zamm.201600023
  • Title of Journal : ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
  • Page Numbers: pp.1600-1610

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. (C) 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim