Generation and Analysis of a New Implicit Difference Scheme for the Korteweg-de Vries Equation

Abstract

In this paper we apply our computer algebra based algorithmic approach to construct a new finite difference scheme for the two-parameter form of the Korteweg-de Vries equation. The approach combines the finite volume method, numerical integration and difference elimination. Being implicit, the obtained scheme is consistent and unconditionally stable. The modified equation for the scheme shows that its accuracy is of the second order in each of the mesh sizes. Using exact one-soliton solution, we compare the numerical behavior of the scheme with that of the other two schemes known in the literature and having the same order of accuracy. The comparison reveals numerical superiority of our scheme.