A mixed algorithm for numerical computation of soliton solutions of the coupled KdV equation: Finite difference method and differential quadrature method

Abstract

The aim of the manuscript is to investigate numerical solutions of the system of coupled Korteweg-de Vries equation. For this approximation, we have used finite difference method for time integration and differential quadrature method depending on modified cubic B-splines for space integration. To display the accuracy of the present mixed method three famous test problems namely single soliton, interaction of two solitons and birth of solitons are solved and the error norms L2 and L∞ are computed and compared with earlier works. Comparison of error norms show that present mixed method obtained superior results than earlier works by using same parameters and less number of nodal points. At the same time, two lowest invariants and amplitude values of solitons during the simulations are calculated and reported. In addition those, relative changes of invariants are computed and tabulated. Properties of solitons observed clearly at the all of the test problems and figures of the all of the simulations are given.