CONSERVATIVE FINITE DIFFERENCE SCHEMES FOR MODIFIED KORTEWEG - DE VRIES EQUATION

摘要

This paper is concerned with the construction of conservative finite difference schemes through a discrete variational method for the modified Korteweg-de Vries equations and the numerical analysis for the modified K-dV equation with the negative coefficients of nolinear terms. A finite difference scheme is proposed such that mass and energy conservation laws associated with the Modified Korteweg-de Vries equations hold. Our arguments are based on the numerical method that D.Furihata has recently developed for real-valued nonlinear partial differential equations. Numerical results are given to assert the accuracy as well as validity of the numberical solutions. Our numerical experiments exhibit remarkable nonlinear phenomena of the interactions and behavior of pulse wave solutions.