Shehu transformation-Akbari Ganji-Padé approximation method for solving Michaelis-Menten nonlinear electrochemical reaction model

Abstract

Nonlinear differential equations play a central role in describing the dynamics of many electrochemical and biological processes. However, due to their inherent complexity, obtaining reliable analytical solutions is often intractable, which necessitates the use of accurate and efficient approximation techniques. In this study, we focus on solving a nonlinear electro-chemical model using the recently proposed fusion approach called Shehu Transformation-Akbari Ganji-Pade Approximation Method (SAGPM). The Euler method, implemented in MATLAB, is employed as a baseline numerical scheme to validate the results. For comparative purposes, we also consider the Kashuri Fundo Decomposition Method (KFDM) and Shehu Transformation-Akbari Ganji Method (SAGM). The findings demonstrate that SAGPM yields solutions that closely agree with the Euler numerical results, thereby confirming its accuracy and reliability. More importantly, SAGPM consistently outperforms both SAGM and KFDM in terms of convergence, stability, and error minimization. In addition, the concentration profiles of the dimensionless state variables $\mathcal{C}(\tau)$ and $\mathcal{I}(\tau)$ exhibit nearly uniform behavior, remaining close to unity across parameter variations, which reflects the robustness of the model. Overall, the study highlights the effectiveness of SAGPM as a hybrid semi-analytical technique that successfully combines computational efficiency with high accuracy. By surpassing the performance of existing methods such as SAGM and KFDM, SAGPM emerges as a powerful tool for addressing nonlinear electro-chemical systems. These results suggest its potential for wider applications in electro-chemical, mathematical biology and other scientific domains where nonlinear dynamics are prevalent.