He’s variational iteration method for solving linear and non-linear systems of ordinary differential equations J. Biazar a, * , H. Ghazvini a,b a Department of Mathematics, Faculty of Sciences, University of Guilan, P.O. Box 1914, P.C. 41938, Rasht, Iran b Department of Mathematics, School of Mathematical Science, Shahrood University of Technology, P.O. Box 316, P.C. 3619995161, Shahrood, Iran Abstract In this article, He’s variational iteration method (VIM) is employed to solve a system of differential equations of first order. Since every ordinary differential equations of higher order can be converted into a system of differential of the first order, this method can be used for solving most differential equations. Some examples are presented to show the ability of the method for linear and non-linear systems of differential equations. The results reveal that the method is very effective and simple. Ó 2007 Published by Elsevier Inc. Keywords: He’s variational iteration method; System of ordinary differential equations 1. Introduction The standard form of a system of ordinary differential equations of the first order with initial conditions is considered as dy 1 dx ¼ f 1 ðx; y 1 ; y 2 ; ... ; y n Þ; y 1 ðx 0 Þ¼ y 1 ; dy 2 dx ¼ f 2 ðx; y 1 ; y 2 ; ... ; y n Þ; y 2 ðx 0 Þ¼ y 2 ; . . . dy n dx ¼ f n ðx; y 1 ; y 2 ; ... ; y n Þ; y n ðx 0 Þ¼ y n ; ð1Þ where each equation represents the first derivative of one of the unknown functions as a mapping depending on the independent variable x, and n unknown functions f 1 ; f 2 ; ... ; f n . 0096-3003/$ - see front matter Ó 2007 Published by Elsevier Inc. doi:10.1016/j.amc.2007.02.153 * Corresponding author. E-mail addresses: biazar@guilan.ac.ir, jbiazar@dal.ca (J. Biazar), hghazvini@guilan.ac.ir (H. Ghazvini). Applied Mathematics and Computation 191 (2007) 287–297 www.elsevier.com/locate/amc