@Article{, title={Efficient Modifications of the Adomian Decomposition Method for Thirteenth Order Ordinary Differential Equations}, author={Samaher M. Yassien}, journal={journal of the college of basic education مجلة كلية التربية الاساسية}, volume={20}, number={87 / علمي}, pages={121-132}, year={2015}, abstract={

Baghdad University,IraqAbstractThis paper deals with the thirteenth order differential equations linear and nonlinear in boundary value problems by using the Modified Adomian Decomposition Method (MADM), the analytical results of the equations have been obtained in terms of convergent series with easily computable components. Two numerical examples results show that this method is a promising and powerful tool for solving this problems.Keywords : Modification adomian decomposition method; Boundary value problems; Linear and Nonlinear Problems; Approximate Solution.1.IntroductionOver the last decade several analytical and approximate methods have been developed to solve the linear and nonlinear differential equations. Among them is the Adomian decomposition method. The Adomian decomposition method has been receiving much attention in recent years in applied mathematics in general, and in the area of series solutions in particular .The method proved to be powerful, effective, and can easily handle a wide class of linear or non-linear, ordinary or partial differential equations, and linear and non-linear integral equations differential delay. The method attacks the problem in a direct way and in a straightforward fashion without using linearization, perturbation or any other restrictive assumption that may change the physical behavior of the model under discussion. Many researchers use ADM to approximate numerical solutions. In [1], Wazwaz proposed a modification of ADM method in series solution to accelerate its rapid convergence, and, in [2] ,Wazwaz also presented several numerical examples of higher-order boundary value problems for first-order linear equation and second-order nonlinear equation by applying modified decomposition method. In addition} }