A Sinc–Galerkin Approximate Solution of the Reaction–Diffusion Process in an Immobilized Biocatalyst Pellet

Abstract

In recent years, an increasing interest has focused on the use of Sinc methods as an essential tools for solving some singular problems arising in different areas of applied sciences. Due to the presence of singularity, these problems raise difficulties in obtaining their analytic or numerical solutions, and various schemes have been proposed to overcome these difficulties. However, among existing approaches, the Sinc methods are well-suited for handling singularity and have high performance on boundary value problems (BVPs) such as problems on unbounded domains or problems with endpoint singularities. In this work, in several geometries and kinetics, an implementation of the Sinc–Galerkin scheme is used to approximate effectiveness factor and concentration profile of key component when a single independent reaction takes place in a porous catalyst structure where enzymes are immobilized. A comparison between the proposed approximated solution and numerical solution reveals that the Sinc–Galerkin method (SGM), as demonstrated with examples, is reliable, accurate and its convergence rate is high.