A Meshless Method of Lines for Numerical Solution of Some Coupled Nonlinear Evolution Equations

摘要

Method of lines (MOL) together with radial basis functions (RBFs) is proposed to find the numerical solution of coupled Korteweg-de Vries (KdV) equations, coupled modified Korteweg-de Vries (mKdV) equations and coupled KdV system. The initial-boudary-value problem is reduced to a system of ordinary differential equations. The system is then solved by the fourth order Runge-Kutta method. Numerical examples are given to illustrate practical usefulness of the present approach. The method is efficient and all the examples take very low CPU time. Accuracy of the method is assessed in terms of L_∞ error norm, number of nodal points and time step size. Superiority of the suggested method is shown through comparison with the spectral collocation method.