A Composition Between Adomian Decomposition Method and Taylor Series Metho in the Series Solution

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Applied Mathematics and Computation 97 (1998) 37~14

A comparison between Adomian decomposition method and Taylor series method in the series solutions

Abdul-Majid W a z w a z 1

Department of Mathematics and Computer Science, Saint Xavier University, 3700 West 103rd Street, Chicago, IL 60655, USA

Abstract In this work, we will compare the performance of the Adomian decomposition method and the Taylor series method applied to the solution of linear and nonlinear ordinary differential equations. The comparison shows that the decomposition method is reliable, efficient and easy to use from a computational viewpoint. Although the two methods provide the solution in an infinite series, the decomposition method provides a fast convergent series of easily computable components and eliminates cumbersome computational work needed by Taylor series method. © 1998 Elsevier Science Inc. All rights reserved.

Keywords." Adomian decomposition method; Taylor series method; Linear and nonlinear differential equations

1. Introduction The Adomian decomposition method [1,2] has been receiving much attention in recent years in the area of series solutions. A considerable research work has been invested recently in applying this method to a wide class of linear and nonlinear equations. A useful attraction of the decomposition method is that it has proved to be a competitive alternative to the Taylor series method and other series techniques. The method has been used in obtaining analytic and

E-mail: wazwaz@sxu.edu. 0096-3003/98/$ - see front matter © 1998 Elsevier Science Inc. All rights reserved. PII: S0096-3003(97) 10127-8

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A.-M. Wazwaz / Appl. Math. Comput. 97 (1998) 37-44

approximate solutions to a wide class of linear and nonlinear, differential and integral equations. In [3], it was found that, unlike other series solution methods, the decomposition method is easy to program in engineering problems, and...