The method of lines solution of the Forced Korteweg-De Vries-Burgers equation (FKdVB)

Abstract

In this paper, the application of the method of lines (MOL) to the Forced Korteweg-de Vries-Burgers equation with variable coefficient (FKdVB) is presented. The MOL is a powerful technique for solving partial differential equations by typically using finite-difference approximations for the spatial derivatives and ordinary differential equations (ODEs) for the time derivative. The MOL approach of the FKdVB equation led to a system of ODEs. Solution of the system of ODEs was obtained by applying the Fourth-OrderRunge-Kutta (RK4) method. In order to show the accuracy of the presented method, the numerical solutions obtained were compared with its progressive wave solution in terms of maximum absolute error at certain times. It was found that the maximum absolute errors are in theorder of 10-6.