Coupling technique of variational iteration and homotopy perturbation methods for nonlinear matrix differential equations

The variational iteration method proposed by Ji-Huan He is a new analytical method to solve nonlinear equations. This paper applies the method to search for exact analytical solutions of linear differential equations with constant coefficients. Furthermore, based on the precise integration method, a coupling technique of the variational iteration method and homotopy perturbation method is proposed to solve nonlinear matrix differential equations. A dynamic system and Burgers equation are taken as examples to illustrate its effectiveness and convenience.