MESHLESS METHOD BASED ON RADIAL BASIS FUNCTIONS FOR GENERAL ROSENAU KdV-RLW EQUATION

Abstract

In the present study, the meshfree RBFs collocation method is used to find the approximate solutions of the general RosenauKdV-RLW equation. Firstly, Crank Nicolson method and forward finite difference approximation method is applied for solvingthe equation. One of the linearization techniques, which is called Rubin graves linearization, is applied for the approximatesolution of the equation. Secondly, the numerical values of physical invariants of the motions for the equation are evaluatedfor studying known fundamental physical conservative properties. Also, to examine the accuracy of the used numerical method𝐿2 and 𝐿∞ norms are evaluated. The stability analysis for the numerical technique is tested. It is seen that the method isunconditionally stable. At the end of this paper, obtained results show the validity and applicability of the numerical method.