A Robust Computational Algorithm for a Class of Nonlinear Enzyme Flow Calorimetric Models Using Taylor Wavelets: An Operational Matrix Method

This paper discusses a mathematical model of the hysteresis behavior of the enzyme-substrate system in enzyme flow calorimetry. The hysteresis of the enzyme-substrate system due to enzyme flow calorimetry is based on the mathematical modeling of an immobilized enzyme system. The models are represented by the nonlinear differential equations of substrate inhibition kinetics in the enzymatic reaction. Two reliable wavelet-based computational algorithms for the approximate solutions for substrate concentration in planar, cylindrical, and spherical particles under steady-state conditions are discussed. To the best of our knowledge, no rigorous wavelet-based solution has been reported for the above models. The main idea of the proposed Taylor Wavelet Method (TWM) is that the nonlinear differential equations are converted into a system of algebraic equations. The validity and applicability of the proposed method are confirmed by comparing the results with those obtained by the Homotopy Perturbation Method (HPM) and the fourth-order Runge-Kutta (RK) method. Satisfactory agreement with the available results is observed. Moreover, the Chebyshev and Taylor wavelet methods are found to be efficient, simple, and straightforward tools for solving nonlinear reaction-diffusion models arising in bioprocess engineering.