Second Order Scheme For Korteweg-De Vries (KDV) Equation

The kinematics of the solitary waves is formed by Korteweg-de Vries (KdV) equation. In this paper, a third order general form of the KdV equation with convection and dispersion terms is considered. Explicit finite difference schemes for the numerical solution of the KdV equation is investigated and stability condition for a first-order scheme using convex combination method is determined. Von Neumann stability analysis is performed to determine the stability condition for a second order scheme. The well-known qualitative behavior of the KdV equation is verified and error estimation for comparisons is performed