Numerical Solution of Kortweg-de Vries Equation

In this paper, we are going to derive numerical methods for solving the KdV equation using Pade approximation for space direction, trapezoidal and implicit mid-point rule in the time direction. The schemes will be analyzed for accuracy and stability. The exact solution and the conserved quantities will be used to display the efficiency and the robustness of the proposed schemes. Interaction of two and three solitons will be conducted. The numerical results showed, interaction behavior is elastic and the conserved quantities are conserved which is a good indication of the reliability of the schemes under consideration.