TY - JOUR
T1 - Numerical solution for a general class of nonlocal nonlinear wave equations arising in elasticity
AU - Muslu, Gulcin M.
AU - Borluk, Handan
N1 - Publisher Copyright:
© 2017 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
PY - 2017/12
Y1 - 2017/12
N2 - 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.
AB - 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.
KW - Boussinesq equations
KW - Convergence
KW - Fourier pseudo-spectral method
KW - Nonlocal nonlinear wave equation
KW - Petviashvili's iteration method
KW - Semi-discrete scheme
UR - http://www.scopus.com/inward/record.url?scp=85021857104&partnerID=8YFLogxK
U2 - 10.1002/zamm.201600023
DO - 10.1002/zamm.201600023
M3 - Article
AN - SCOPUS:85021857104
SN - 0044-2267
VL - 97
SP - 1600
EP - 1610
JO - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
JF - ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik
IS - 12
ER -