Numerical Soliton Solution for GRRLW Equation Using Fifth Order Runge-Kutta and Higher Order B-Spline Collocation Schemes

Abstract

In this work, an efficient numerical method is proposed to obtain the approximate solution of the general Rosenau regularised long wave equation. The present method based on Butcher’s fifth-order Runge-Kutta scheme, which consider a septic B-spline as the basis function, respectively. In this method, the approximate solutions are measured by neither transformation nor any kind of linearization technique to tackle the non linearity. Butcher’s fifth-order Runge-Kutta approach without using a finite difference scheme at each time level is implemented for the numerical treatment of a system of first-order differential equations. The linear stability for the linearized septic B-spline scheme is investigated. The error norms are calculated on problem to enhance efficiency and accuracy of the present method and also compared to the existing results.