Modification of Homotopy Perturbation method for addressing systems of PDEs

Abstract

This work employs a refined variation of the Homotopy Perturbation Method (HPM), termed the Modified Homotopy Perturbation Method (MHPM), designed to obtain accurate solutions for significant systems of partial differential equations (PDEs). By incorporating Laplace transforms and Padé approximants, MHPM achieves enhanced convergence and precision with minimal computational overhead, overcoming limitations of traditional perturbation techniques. We extend MHPM to solve more intricate nonlinear systems, showcasing its adaptability and robustness through applications to Burgers’ equations and the Brusselator model. These examples highlight MHPM’s utility in accurately resolving dynamic systems with real-world implications, including fluid flows, reaction kinetics, and engineering models, where computational efficiency and solution precision are critical.