Numerical method for the wave and nonlinear diffusion equations with the homotopy perturbation method
In this paper, the homotopy perturbation method and a modified homotopy perturbation method are used for analytical treatment of the wave equation and some nonlinear diffusion equations, respectively. Some examples are given to illustrate that a suitable choice of an initial solution can lead to the exact solution, this revealing the reliability and effectiveness of the method.
nonlinear diffusion equations homotopy perturbation method wave equation exact solutions hes polynomials dalembert formula approximate analytical solution