A NEW KIND OF UNIVERSAL DIFFERENCE SCHEMES FOR SOLVING KDV EQUATION

摘要

This paper is based on a typical model for non-linear dispersion equation (KdV equation). Construct two new kinds of the more universal three-time and two-time difference scheme, and give a new method for determining the computational stability of two kinds of difference schemes. Numerical experiment proves practical and effective. The stability criteria which are obtained are indeed a necessary condition; the results prove the two-time difference scheme is more stable than three-time difference scheme, three-time difference scheme is prone to computational instability and the two-time difference scheme is prone to computational stability. Two schemes don't produce the non-linear computational instability, and only results in the linear computational instability. This paper finds when the parameter takes 2/3; the two-time difference scheme has the advantage of high accuracy.