In this article, the Homotopy Perturbation Method (HPM) is employed to approximate solutions of a modified Lotka–Volterra equation. HPM has been introduced by He to solve approximately linear or nonlinear differential equations. Approximate polynomials have also been constructed to find approximate solutions of a modified Lotka-Volterra system. Numerical comparisons are made between HPM and maple numerical results.

This paper applies the homotopy perturbation method (HPM) to find the exact solution of Poisson equation with the Dirichlet and Neumann boundary conditions. To illustrate the simplicity and reliability of the method, two examples are provided. The results obtained reveal that the method is capable and easy to apply.

More recently, Wazwaz [An analytic study of Fisher’s equation by using Adomian decomposition method, Appl. Math. Comput.154 (2004) 609–620] employed the Adomian decomposition method (ADM) to obtain exact solutions to Fisher’s equation and to a nonlinear diffusion equation of the Fisher type. In this paper, He’s homotopy perturbation method is employed for the generalized Fisher’s equation to overcome the difficulty arising in calculating Adomian polynomials.

This paper applies homotopy perturbation method (HPM) to find the exact solution of Poisson equation with Dirichlet and Neumann boundary conditions. To illustrate the simplicity and reliability of the method, two examples are provided. The results obtained reveal that the method is capable and easy to apply.

In this paper we use the Homotopy perturbation method (HPM) to comput the Maclaurin series of the given function y=f(x). First, we form an equation like A(f)=0, for the given function y=f(x). Afterward, we solve this equation by using the Homotopy perturbation method. Finally, we verify simplicity and efficiency our method by some examples.