On the numerical solutions to nonlinear biochemical reaction model using Picard-Padé technique

In this paper, we introduce a modification of the Picard iteration method (PIM) using Padé approximation and so called Picard-Padé technique. Special attention is given to study the convergence analysis of the proposed method. Convergence analysis is reliable enough to estimate the maximum absolute error of the solution given by PIM. A basic enzyme kinetics is used to test the effectiveness of the proposed method. This enzyme-substrate reaction is formed by a system of nonlinear ordinary differential equations. We compare our numerical results against the conventional numerical method, fourth-order Runge-Kutta method (RK4). Numerical results were obtained for these two methods and we found that Picard-Padé technique and RK4 are in excellent conformance. The results obtained ensure that the presented procedure needs less work in comparison with the traditional methods and decreases considerable volume of calculation and a powerful tool for solving large amount of other problems in physics and engineering.