Numerical investigation of nonlinear generalized regularized long wave equation via delta-shaped basis functions

Abstract

In this study we will investigate generalized regularized long wave (GRLW)equation numerically. The GRLW equation is a highly nonlinear partial differential equation. We use finite difference approach for time derivatives andlinearize the nonlinear equation. Then for space discretization we use deltashaped basis functions which are relatively few studied basis functions. Bydoing so we obtain a linear system of equations whose solution is used for constructing numerical solution of the GRLW equation. To see efficiency of theproposed method four classic test problems namely the motion of a single solitary wave, interaction of two solitary waves, interaction of three solitary wavesand Maxwellian initial condition are solved. Further, invariants are calculated.The results of numerical simulations are compared with exact solutions if available and with finite difference, finite element and some collocation methods.The comparison indicates that the proposed method is favorable and givesaccurate results.