Differential Transform Method for Nonlinear Initial-Value Problems by Adomian Polynomials
S. H. Behiry*
General Required Courses Department, Jeddah Community College, King Abdulaziz University, Jeddah 21589, Kingdom of Saudi Arabia
- *Corresponding Author:
- S. H. Behiry
General Required Courses Department
Jeddah Community College, King Abdulaziz University
Jeddah 21589, Kingdom of Saudi Arabia
E-mail: [email protected]
Received Date: April 17, 2012; Accepted Date: May 15, 2012; Published Date: May 19, 2012
Citation: Behiry SH (2012) Differential Transform Method for Nonlinear Initial-Value Problems by Adomian Polynomials. J Appl Computat Math 1:109. doi: 10.4172/2168-9679.1000109
Copyright: ©2012 Behiry SH. 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.
In this paper, the differential transformation method is modified to be easily employed to solve wide kinds of nonlinear initial-value problems. In this approach, the nonlinear term is replaced by its Adomian polynomials for the index k, and hence the dependent variable components are replaced in the recurrence relation by their corresponding differential transform components of the same index. Thus the nonlinear initial-value problem can be easily solved with less computational effort. New theorems for product and integrals of nonlinear functions are introduced. In order to show the power and effectiveness of the present modified method and to illustrate the pertinent features of related theorems, several numerical examples with different types of nonlinearities are considered.