On the numerical solutions for chemical kinetics system using Picard–Padé technique

In this Letter, we introduced a modification of the Picard iteration method (PIM) using Padé approximation and the so called Picard–Padé technique. This technique is used to solve the chemical kinetics problem. This problem is formed by a system of nonlinear ordinary differential equations. 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. We compared 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 is a powerful tool for solving large amount of other problems in physics and engineering.