A reliable method for the numerical solution of the kinetics problems - Kaya, D (Elsevier Science Inc, 2004)
This paper deals with the implementation of the Adomian's decomposition method in chemical applications one often encounters systems of ordinary differential equations. This method is intended to solve the approximate solutions of the linear and nonlinear kinetic problems without usual restrictive assumptions. A new approach to differential problems is particularly valuable as a tool for Scientists and Applied Mathematicians, because it provides immediate and visible symbolic terms of analytic solution as well as its numerical approximate solution to both linear and nonlinear problems without linearization Adomian [Solving Frontier Problems of Physics: The Decomposition Method, Kluwer Academic Publishers, Boston, 1994; J. Math. Anal. Appl. 135 (1988) 501]. It does also not require discretization and consequently massive computation. We also give a comparison between a reliable decomposition and a conventional methods such as the Taylor series and the fourth-order Runge-Kutta method for system of ordinary differential equations. The numerical results demonstrate that the new method is quite accurate and readily implemented. (C) 2003 Elsevier Inc. All rights reserved.
Keywords: the decomposition method; the Taylor series method; the fourth-order Runge-Kutta method; kinetic problems