Efficient solutions for modeling nonlinear enzyme reaction dynamics using DTM, CPEM and NSFD

Abstract

The dynamics of non-linear enzyme reaction is fundamental to understanding complex biochemical processes, but their intricate nature presents significant challenges for accurate modeling and analysis. This study investigates the performance of two analytical methods: the Differential Transform Method (DTM) and the Chebyshev Polynomial-Exponential Method (CPEM) in solving system of nonlinear reaction equations, comparing their outcomes with those derived from the Non-Standard Finite Difference (NSFD) numerical method. The primary objective of this research is to explore the behavior of the enzyme reaction system under varying dimensionless parameters by transforming the governing first-order differential equations into a dimensionless framework. 
Motivated by the demand for precise and efficient modeling approaches, the study evaluates the accuracy, computational efficiency, and practical applicability of these methods. The results reveal that both DTM and CPEM deliver effective approximate solutions, with CPEM demonstrating exceptional precision and stability relative to NSFD. These findings underscore the synergistic potential of combining analytical and numerical techniques, offering advanced tools for the study of enzyme kinetics, and improving predictive precision in biochemical research. This work contributes to the development of robust methodologies for addressing the complexities inherent in modeling nonlinear biochemical systems.