Non-isothermal Reaction–Diffusion Model Equations in a Spherical Biocatalyst: Green’s Function and Fixed Point Iteration Approach

Abstract

A second order singular boundary value problem that occurs in biochemical reaction–diffusion process has been studied and tackled numerically by many scholars. In this article, a new approach is presented then applied to solve this problem with very successful results. A recent and relatively established strategy that embeds Green’s function into Picard–Mann’s fixed point schemes has been implemented to handle the ordinary differential equation. The Green’s function that is constructed, is necessary to overcome the complicated term of the equation, namely the one that possesses the singularity. The numerical experiments confirm the efficiency and applicability of the proposed method.