Fourth-Order Conservative Algorithm for Nonlinear Wave Propagation: the Rosenau-KdV Equation

Rakbhoom Chousurin, Thanasak Mouktonglang, Phakdi Charoensawan

Abstract

In this paper, we introduce  a conservative difference method for solving the Rosenau-KdV equation.  The existence of the approximate solution from the difference scheme is shown. We also prove the stability and convergence of this scheme. The presented method gives second- and fourth-order accurate in time and space, respectively. Numerical examples demonstrate the theoretical results.