On the numerical study of the KdV equation by the Semi-Implicit and Leap-frog Method Original Research Article

A numerical study of the Korteweg-de Vries (KdV) Equation by means of a new but simple scheme, called the Semi-Implicit Method (SIM), is presented in this paper. The basic idea behind the SIM is to approximate the nonlinear term in the original equation by a product of terms in the previous and present time steps. Comparison of this scheme to the well-known Leap-frog Method (LFM) proposed by Zabusky et al. shows that the SIM is a faster scheme. Besides, it is an unconditionally stable method whereas the LFM is only a conditionally stable scheme.