Volume 4 • Issue 1 • 1000199 J Appl Computat Math ISSN: 2168-9679 JACM, an open access journal Open Access Research Article Applied & Computational Mathematics ISSN: 2168-9679 J o u r n a l o f A p p li e d & C o m p u t a t i o n a l M a t h e m a t i c s Jameel, J Appl Computat Math 2015, 4:1 http://dx.doi.org/10.4172/2168-9679.1000199 Keywords: Fuzzy numbers; Fuzzy diferential equations; Two point fuzzy boundary value problems; Adomian decomposition method Introduction Many dynamical real life problems may be formulated as a mathematical model. Many of them can be formulated either as a system of ordinary or partial diferential equations. Fuzzy diferential equations (FDEs) are a useful tool to model a dynamical system when information about its behavior is inadequate. FDE appears when the modeling of these problems was imperfect and its nature is under uncertainty. FDEs are suitable mathematical models to model dynamical systems in which there exist uncertainties or vagueness. hese models are used in various applications including, population models [1-3], mathematical physics [4], and medicine [5,6]. In recent year’s semi -analytical methods such as the Adomian Decomposition Method (ADM), Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM), Optimal Homotopy asymptotic method (OHAM) and Homotopy Analysis Method (HAM) have been used to solve fuzzy irst and n th order ordinary diferential equations. For n th order fuzzy initial value problems, he ADM was employed in [7] to solve second order linear fuzzy initial value problems. Abbasbandy et al. [8] used the VIM to solve linear system of irst order fuzzy initial value problems. Moreover, some of these methods have been also used to obtain a semi-analytical solution of TPFBVP. VIM has been used in [9] to solve linear TPFBVP. Other method like undetermined fuzzy coeicients method has been introduced in [10] in order to obtain an approximate solution of second order linear TPFBVP. he ADM have been introduced in [11,12] and has been applied to a wide class of deterministic and stochastic problems of mathematical and physical sciences [13-15]. his method provides the solution as a rapidly convergent series with components that are elegantly computed. his method can be used to solve all types of linear and nonlinear equations such as diferential and integral equations, so it is known as a powerful method. Another important advantage of this method is that it can reduce the size of computations, while increases the accuracy of the approximate solutions so it is known as a powerful method In this paper, our aim is to formulate ADM from crisp into fuzzy case in order to solve nonlinear n th order TPFBVP directly. To the best of our knowledge, this is the irst attempt at solving the n th order TPFBVP using the ADM. he structure of this paper is as follows: In section 2, some basic deinitions and notations are given about fuzzy numbers that will be used in other sections we discussed. In section 3, the structure of ADM is formulated for solving high order TPFBVP. In section 4, we present a numerical example and inally, in section 5, we give the conclusion of this study Figure 1. Fuzzy Numbers Fuzzy numbers are a subset of the real numbers set, and represent uncertain values. Fuzzy numbers are linked to degrees of membership which state how true it is to say if something belongs or not to a determined set Figure 2. A fuzzy number [16] µ is called a triangular fuzzy number if deined by three numbers α<β<γ where the graph of (x) µ is a triangle with the base on the interval [α,β] and vertex at x , =β and its membership function has the following form: ( ) 0, x , x; x , 1, α α β β γ <   −α  ≤ ≤ β−α  µ α,β,γ =  γ−  ≤ ≤ γ−β  >  if x if x if x y if x *Corresponding author: Jameel AF, School of Mathematical Sciences, 11800 USM, University Science Malaysia, Tel: 6046533888; E-mail: kakarotte79@gmail.com Received September 10, 2014; Accepted December 29, 2014; Published January 10, 2015 Citation: Jameel AF (2015) Semi Analytical-Solution of Nonlinear Two Points Fuzzy Boundary Value Problems by Adomian Decomposition Method. J Appl Computat Math 4: 199. doi:10.4172/2168-9679.1000199 Copyright: © 2015 Jameel AF. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Abstract In this paper the Adomian Decomposition Method (ADM) is employed to solve n th order (n>2) non linear two point fuzzy boundary value problems (TPFBVP). The Adomian decomposition method can be used for solving nth order fuzzy differential equations directly without reduction to irst order system. We illustrate the method in numerical experiment including fourth order nonlinear TPFBVP to show the capabilities of ADM. Semi Analytical-Solution of Nonlinear Two Points Fuzzy Boundary Value Problems by Adomian Decomposition Method Jameel AF* School of Mathematical Sciences, 11800 USM, University Science Malaysia, Penang, Malaysia α β x µ (x) 1 0 0.5 γ Figure 1: Triangular Fuzzy Number.