Bulletin of Mathematics Vol. 04, No. 01 (2012), pp. 1–15. THE EXACT SOLUTION OF DELAY DIFFERENTIAL EQUATIONS USING COUPLING VARIATIONAL ITERATION WITH TAYLOR SERIES AND SMALL TERM Y.M. Rangkuti and M.S.M. Noorani Abstract. This study investigated the applicability of coupling the variational it- eration method (VIM) with Taylor series and small term for exact of delay differ- ential equations (DDEs). VIM uses general Lagrange multipliers for constructing the correction functional for the problems. For this work, it is assumed that terms with delay are considered as restricted variations and also gives Taylor approach and ignoring a small term on VIM. The analytical solutions for various examples are obtained by this method. The results obtained show that these algorithms are accurate and efficient for the solution of DDEs. 1. INTRODUCTION In mathematics, delay differential equations (DDEs) is type of differ- ential equations in which the derivative of the unknown function at a certain time t is given in terms of the values at an earlier time ξ (t). In this paper, delay differential equations are considered, DDEs in the form: u (n) (t)= f (t, u (i) (t),u(ξ (t))), (1) Received 28-11-2011, Accepted 05-12-2011. 2010 Mathematics Subject Classification: 65D25; 40A25; 92B05. Key words and Phrases: variational iteration method; delay differential equations; Taylor series; Small term; Lagrange multiplier. 1