A hybrid numerical method for the KdV equation by finite difference and sinc collocation method

Abstract

In this paper, we propose a hybrid numerical method for the KdV equation. More precisely, we discretize the temporal derivative of KdV equation by a θ-weighted scheme and treat the implicitly nonlinear term with the combination of finite difference and sinc collocation method. The stability analysis is presented, and numerical experiments illustrate the efficiency and stability of the proposed hybrid method. The motions and the interactions of solitary waves relying on particular initial boundary conditions are also simulated.