The method of lines solution of the Forced Korteweg-de Vries-Burgers equation

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 leads to a system of ODEs. The solution of the system of ODEs is obtained by applying the Fourth-Order Runge-Kutta (RK4) method. The numerical solution obtained is then compared with its progressive wave solution in order to show the accuracy of the MOL method