Numerical Solution of Korteweg-de Vries Equation by the Fourier Pseudospectral Method

Abstract

In this paper, we present a numerical solution of one-dimensional Korteweg-de Vries equation with variant boundary conditions by the Fourier pseudospectral method. Four test problem with known exact solutions were studied to demonstrate the accuracy of the present method. An artificial viscosity was proposed to improve the accuracy of the numerical scheme. The obtained results were compared with the exact solution of each problem and found to be in good agreement with each other.