Numerical solution for a general class of nonlocal nonlinear wave equations arising in elasticity. Issue 12 (7th July 2017)

• Record Type: Journal Article
• Authors: Muslu, Gulcin M.; Borluk, Handan
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 97:Issue 12(2017)
• Page Start: 1600
• Page End: 1610
• Publication Date: 2017-07-07
• Subjects: Nonlocal nonlinear wave equation -- Boussinesq equations -- Fourier pseudo‐spectral method -- Semi‐discrete scheme -- Convergence -- Petviashvili's iteration method -- 65M70 -- 35C07; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.201600023
• Languages: English
• ISSNs: 0044-2267

Abstract

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. 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. The authors discretize the equation by using Fourier spectral method in space and they prove the convergence of the semidiscrete scheme. They 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, they use the Petviashvili's iteration method.