Coupling technique of variational iteration and homotopy perturbation methods for nonlinear matrix differential equations
2007
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.
Keywords:
- Mathematical optimization
- Examples of differential equations
- Mathematical analysis
- Homotopy analysis method
- Poincaré–Lindstedt method
- Partial differential equation
- Mathematics
- Numerical partial differential equations
- Stiffness matrix
- Spectral method
- Nonlinear system
- Adomian decomposition method
- Differential algebraic equation
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