Alternating segment explicit-implicit scheme for nonlinear third-order KdV equation

Abstract

A group of asymmetric difference schemes to approach the Korteweg-de Vries (KdV) equation is given here. According to such schemes, the full explicit difference scheme and the full implicit one, an alternating segment explicit-implicit difference scheme for solving the KdV equation is constructed. The scheme is linear unconditionally stable by the analysis of linearization procedure, and is used directly on the parallel computer. The numerical experiments show that the method has high accuracy.