Numerical solutions of generalized <scp>Rosenau–KDV–RLW</scp> equation by using Haar wavelet collocation approach coupled with nonstandard finite difference scheme and quasilinearization
Amit K. Verma, Mukesh Kumar Rawani
Abstract
Abstract In this article, we analyze and propose to compute the numerical solutions of a generalized Rosenau–KDV–RLW (Rosenau‐Korteweg De Vries‐Regularized Long Wave) equation based on the Haar wavelet (HW) collocation approach coupled with nonstandard finite difference (NSFD) scheme and quasilinearization. In the process of the numerical solution, the NSFD scheme is applied to discretize the first‐order time derivative, Haar wavelets are applied on spatial derivatives and the non‐linear term is taken care by quasilinearization technique. To discuss the efficiency of the method we compute error and error. We also use discrete mass and energy conservation to check the accuracy of the proposed methodology. The computed results have been compared with the existing methods, for example, three‐level average implicit finite difference technique, B‐spline collocation, three‐level linear conservative implicit finite difference scheme and conservative fourth‐order stable finite difference scheme.