A reliable Taylor series solution to the nonlinear reaction-diffusion model representing the steady-state behaviour of a cationic glucose-sensitive membrane

Abstract

The nonlinear reaction-diffusion model, which represents the steady-state behaviour of a cationic glucose-sensitive membrane with consideration of oxygen limitation and swelling-dependent diffusivities of involved species inside the membrane, is discussed. Analytical expressions of substrate concentration of oxygen, glucose, and gluconic acid in planar coordinates at steady-state conditions are derived for all kinetic parameters, and hence the effect of various factors on the responsiveness of the membrane is analysed. Efficient approaches based on the hyperbolic function and Taylor’s series methods are used to derive the approximate analytical solutions of the nonlinear boundary value problem. A numerical simulation was generated by highly accurate and widely used computer generated routines. The derived analytical expressions are shown to be in strong agreements with the numerical results established in the literature. It is concluded that each method is a powerful tool for solving high-order boundary value problem in engineering and science.