Convergence Analysis of Three-Level Fourier Pseudospectral Method for Korteweg-de Vries Burgers Equation

In this paper, a Fourier pseudospectral method for numerical approximation of a periodic initial boundary value problem for the Korteweg-de Vries Burgers equation is developed. The finite difference method is used in time direction, while the pseudospectral method is used in x-direction. A modified leapfrog scheme is constructed in such a way that the linear part is treated implicitly and the nonlinear part explicitly. The stability and rate of convergence for the scheme are proved. The numerical results are presented, which verify the theoretical arguments.