The International Journal of Medical Discoveries (IJMD) is a peer-reviewed, open-access journal dedicated to advancing the understanding, innovation, and application of medical science. Our mission is to serve as a platform for the dissemination of cutting-edge research and discoveries that shape the future of healthcare and important medical discoveries worldwide.
The Homotopy Perturbation Method is among the most effective analytical methods for solving nonlinear partial differential equations with various boundary conditions. In this study, the strengths and weaknesses of the HPM will be presented, as well as the use of HPM combined with other techniques, like the Laplace transform and the Sumudu transform, in solving nonlinear partial differential equations. The study will also compare the accuracy, convergence, and applicability of the Homotopy Perturbation Method with the Adomian Decomposition Method and the Variational Iteration Method based on the literature review. The study reveals that HPM provides a high convergence rate and accuracy and can handle different boundary conditions, making it more effective than other numerical approaches. The study finds that other advancements in the HPM, including the Delta HP Method, will enhance the efficacy of solutions of nonlinear partial differential equations in various fields. As much as the Homotopy Perturbation Method is efficient in providing solutions to nonlinear partial differential equations, challenges have been noted while using the method for equations with high-frequency solutions as well as non-elementary boundary conditions. Further improvement of the Homotopy Perturbation Method is recommended for solving nonlinear partial differential equations, and this method can be used in combination with other methods to expand the range of its application.
Homotopy perturbation method, Homotopy perturbation theory, Partial differential equations, Numerical solutions