A comparative study of Haar Wavelet Method and Homotopy Perturbation Method for solving one-dimensional Reaction-Diffusion Equations

摘要

Abstract—In this paper, we introduce a homotopy perturbationmethod to obtain exact solutions to some linear and nonlinear onedimensional reaction-diffusion equations. This method is a powerful device for solving a wide variety of problems. Using the homotopy perturbation method, it is possible to find the exact solution or an approximate solution of the problem. The power of this manageable method is confirmed. An attempt is made to combine the advantages of the Homotopy Perturbation Method (HPM) and Haar wavelets.Good agreement with the exact solution has been observed. The results reveal that the HPM and HWM are very effective, convenient and quite accurate to systems of partial differential equations. It is predicted that the HWM and HPM can be found widely applicable in engineering.