A handy approximation for a mediated bioelectrocatalysis process, related to Michaelis-Menten equation

Area of Science:

• Applied Mathematics
• Chemical Kinetics
• Biochemical Engineering

Background:

• Nonlinear reaction-diffusion equations are crucial for modeling complex phenomena in various scientific fields.
• Michaelis-Menten kinetics describes enzyme-catalyzed reactions, often introducing nonlinearity.
• Finding exact solutions for such equations can be analytically challenging.

Purpose of the Study:

• To apply the Perturbation Method (PM) for an approximate solution to steady-state nonlinear reaction-diffusion equations.
• To incorporate a nonlinear term based on Michaelis-Menten enzymatic kinetics.
• To validate the efficiency and accuracy of the PM by comparing it with exact solutions.

Main Methods:

• The Perturbation Method (PM) was utilized to derive an approximate analytical solution.
• The study focused on steady-state conditions for the reaction-diffusion equation.
• Graphical analysis was performed to compare the approximate PM solution with the exact solution.

Main Results:

• The Perturbation Method yielded a practical approximate solution for the specified nonlinear reaction-diffusion equation.
• The presence of the Michaelis-Menten term was effectively handled by the method.
• Visual comparisons demonstrated a high degree of agreement between the approximate and exact solutions.

Conclusions:

• The Perturbation Method is an effective and efficient technique for solving nonlinear reaction-diffusion equations with Michaelis-Menten kinetics.
• The PM offers a valuable tool for approximating solutions where exact solutions are difficult to obtain.
• This study highlights the applicability of the PM in biochemical and chemical engineering contexts.