Comparison Of Several Numerical Methods For The KdV Equation

This article focuses on the numerical methods for Korteweg-de Vries(KdV)equation. We use the finite difference method, DDG method and LDG method for space discretization and the Crank-Nicolson method for time discretization. We first present the above numerical schemes for the KdV equation, and then show their conservation properties for both semi-discrete schemes and full-discrete schemes.Finally, through several typical numerical examples, the numerical performance of these methods is investigated from the aspects of convergence, stability and the conservation of the equation. The numerical results show that DDG and LDG method are better than the finite difference method.