Spectral solutions for a class of nonlinear wave equations with Riesz fractional based on Legendre collocation technique

Abstract

A numerical investigation is presented in this work for a class of Riesz space-fractional nonlinear wave equations (MD-RSFN-WEs). The presence of a spatial Laplacian of fractional order, stated by fractional Riesz derivatives, is taken into consideration by the model. The fractional wave equation governs mechanical diffusive wave propagation in viscoelastic medium with power-law creep and, as a result, gives a physical understanding of this equation within the context of dynamic viscoelasticity. To deal with the independent variables, a totally spectral collocation approach is used. Our approach has shown to be more precise, efficient, and practical for the present model. The findings demonstrated that the spectral scheme is exponentially convergent.