Numerical Solution for Fuzzy Enzyme Kinetic Equations by the Runge–Kutta Method

Yousef Barazandeh,Bahman Ghazanfari

doi:10.3390/mca23010016

Abstract

One of the most important biochemical reactions is catalyzed by enzymes. A numerical method to solve nonlinear equations of enzyme kinetics, known as the Michaelis and Menten equations, together with fuzzy initial values is introduced. The numerical method is based on the fourth order Runge–Kutta method, which is generalized for a fuzzy system of differential equations. The convergence and stability of the method are also presented. The capability of the method in fuzzy enzyme kinetics is demonstrated by some numerical examples.

Highlights

Enzymes found in nature have been used since ancient times in the production of food products
In 1913, Michaelis and Menten offered a simple model for enzyme reaction, as seen below [3,5,6]
Given the examples with different values of parameters and fuzzy initial values in Equation (12), we plot the approximation of C(t), S(t)

Summary

Introduction

Enzymes found in nature have been used since ancient times in the production of food products. [23] If fi(t, u1, ..., un) for i = 1, 2, ..., n are continuous functions of t and satisfy the Lipschitz condition in u = (u1, ..., un)t in the region D = {(t, u)|t ∈ I = [0, 1], −∞ < ui < ∞ for i = 1, 2, ..., n} with constant Li, the initial value problem (5) has a unique fuzzy solution in each case. 4. Fuzzy Runge–Kutta Method of Order Four for the Fuzzy Kinetic Enzyme Reaction Consider Equation (2) in which the initial values are fuzzy, i.e., λS(t).

Convergence and Stability

Examples

Conclusions