An efficient approximation algorithm for the nonlinear reaction: diffusion equations in an electro catalytic thin film models using Hosoya polynomials

Abstract

The paper discusses a mathematical model for non-Michaelis–Menten kinetics, which involves a substrate forming a complex with the immobilized catalyst. A new Hosoya polynomial approximation method (HPAM) is applied for solving the reaction–diffusion equations. Analytical expressions are established to the nonlinear reaction–diffusion equation arising in electro catalytic thin film with an arbitrary shape models using the Hosoya polynomials. The main idea of the proposed research work is that the nonlinear reaction–diffusion problems are converted into a system of algebraic equations using the Hosoya polynomials. Analytical expressions for substrate concentration profiles are derived in closed and simplified forms for various geometries (planar, cylindrical, and spherical), along with the corresponding steady-state amperometric current response. The proposed results are validated with the other available results. Moreover, the utility of HPAM is investigated to be simple, straight forward, efficient and flexible. Also, the paper examines how different parameters influence the substrate concentration in the above models.