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

Abstract

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 y error norm, number of nodal points and time step size. Superiority of the suggested method is shown through comparison with the spectral collocation method.

Lattice Boltzmann model for a class of coupled nonlinear partial differential equations with variable coefficients

“…The fundamental equations of many important physics and mechanics disciplines are NLPDEs, and their analytical solutions can help us better understand complex physical phenomena and mechanisms. Over the past few decades, many numerical methods have been developed to solve NLPDEs, such as finite element method [3,4], finite volume method [5,6], finite difference method [7][8][9], spectral method [10,11] and meshless method [12][13][14][15], etc.…”