Chebyshev and Legendre via Galerkin method for solving KdV Burgers' equation

Abstract

In this paper, three numerical solutions for the Kortewegde Vries Burgers' (KdVB) equation are presented. Two of these methods are based on cardinal Chebyshev basis function with Galerkin method. Gauss-quadrature formula and El-gendi method are used to convert the problem into system of ordinary differential equations. In the third proposed method, the cardinal Legendre basis function with Galerkin method is used. In this case, the approximations are based on El-gendi method. The numerical results obtained by these ways have been compared with other solutions by Darvishi's preconditioning to the same problem to show the efficiency of the proposed methods.