Modification of quintic B-spline differential quadrature method to nonlinear Korteweg-de Vries equation and numerical experiments

Abstract

In this manuscript, a novel modification of quintic B-spline differential quadrature method is given. By this modification, the obtained algebraic system do not have any ghost points. Therefore, the equation system is solvable and doesn't need any additional equation. Another advantage of this modification is the fact that the obtained numerical results are better than classical methods. Finite difference method is used as another component of the algorithm to obtain numerical solution of Korteweg-de Vries (KdV) equation which is the important model of nonlinear phenomena. Nine effective experiments namely single soliton, double solitons, interaction of two solitons, splitting to the solitons, interaction of three-, four-, and five solitons, evolution of solitons via Maxwellian initial condition and train of solitons are given with comparison of error norms and invariants. All of the given results with earlier studies show that the present scheme has improved classical common methods. Rate of convergence for single soliton and double solitons problems are reported.