He-Laplace variational iteration method for solving the nonlinear equations arising in chemical kinetics and population dynamics

In this article, we suggest an alternative approach for the study of some partial differential equations (PDEs) arising in physical phenomena such as chemical kinetics and population dynamics. He-Laplace variational iteration method (He-LVIM) is a simple but effective way where the variational iteration method (VIM) is coupled with Laplace transforms method. He's polynomials are obtained by the homotopy perturbation method (HPM) to deal with the nonlinear terms. Fisher equation, the generalized Fisher equation and the nonlinear diffusion equation of the Fisher type are suggested to demonstrate the accuracy and stability of this method.

Automated summary

This article introduces an alternative method for studying partial differential equations, known as the He-Laplace variational iteration method. The method combines variational iteration method with Laplace transforms method, and employs He's polynomials obtained by the homotopy perturbation method to handle nonlinear terms. The accuracy and stability of this method are demonstrated on Fisher equation, generalized Fisher equation, and the nonlinear diffusion equation of the Fisher type.