Numerical Solution of the Rosenau-KdV-RLW equation via combination of a polynomial scaling function collocation and finite difference method

Abstract

In this paper, we established a polynomial scaling method to investigate the numerical solution of Rosenau–Korteweg De Vries-regularized long wave (Rosenau-KdV-RLW) equation. We start with discretization of the time variable of the equation using a finite difference approach equipped with a linearization. After the time discretization, we have used polynomial scaling functions for the discretization of the spatial variable. These two discretizations give us the desired discrete system of equations to obtain numerical solutions. We further derive an error estimate for the proposed method. We have applied the proposed method to Rosenau-KdV, Rosenau-RLW, and Rosenau-KdV-RLW equations and used error norms to examine the accuracy and reliability of the presented method. Also, to enhance accuracy of the results, we utilize Richardson extrapolation. The comparisons with the analytical solution and earlier studies that use different methods indicate that the proposed method is accurate and reliable.