Series Solution of 3D Unsteady Reaction Diffusion Equations Using Homotopy Analysis Method

Abstract

          This study aims to verify and suggest the use of the Homotopy Analysis Method (HAM) as a flexible and reliable method to handle the difficulties involved in solving 3D unsteady reaction-diffusion equations. Reaction-diffusion equations are essential to the modeling of many real-world processes in many academic fields. Yet, they are still quite difficult to solve, especially in three dimensions and under unstable circumstances. In the current study, we provide an organized process for building the homotopy operator; we take the solution and make it into a series. Then, we use the homotopy perturbation approach to improve repeatedly. We illustrate the accuracy of our method in approximating solutions to the reaction-diffusion equations via a series of comprehensive numerical experiments. The accuracy is highlighted by the numerical results. We carry out an extensive convergence study to confirm the correctness and dependability of the answers, confirming the legitimacy of methodology and emphasizing its possible benefits over current approaches. The study provides important insights into the behavior of such systems and builds a strong computational foundation for future studies that will examine more complicated and dynamic systems. This research advances our knowledge of reaction-diffusion processes.