• APPLICATION OF THE MULTIGRID TECHNIQUE FOR THE NUMERICAL SOLUTION OF THE NON-LINEAR DISPERSIVE WAVES EQUATIONS

Abstract

The scope of this paper is to obtain the numerical solutions of the Korteweg-de Vries (KdV) equation and the related partial differential equations (namely: the modified Korteweg-de Vries equation (MKdV) and the Korteweg-de Vries-Burgers' equation (KdVB)) using the multigrid method. The difference equation of the Korteweg-de Vries (KdV) equation and the related partial differential equations using the finite difference method are obtained. The computer cods are used to obtain the numerical solutions that compared with the analytical ones to get the -errors. The obtained results are compared with another method using -errors to show the deviation between them.