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, cilt.97, sa.12, ss.1600-1610, 2017 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 97 Konu: 12
  • Basım Tarihi: 2017
  • Doi Numarası: 10.1002/zamm.201600023
  • Dergi Adı: ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
  • Sayfa Sayıları: ss.1600-1610

Özet

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