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LARGE INTERVAL SOLUTION OF THE EMDEN–FOWLER EQUATION USING A MODIFIED ADOMIAN DECOMPOSITION METHOD WITH AN INTEGRATING FACTOR

Part of: Numerical analysis: Ordinary differential equations

Published online by Cambridge University Press:  15 December 2014

YINWEI LIN ,
TZON-TZER LU  and
CHA’O-KUANG CHEN
YINWEI LIN
Affiliation:
Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan email timothy@math.nsysu.edu.tw, ttlu@math.nsysu.edu.tw
TZON-TZER LU*
Affiliation:
Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan email timothy@math.nsysu.edu.tw, ttlu@math.nsysu.edu.tw
CHA’O-KUANG CHEN
Affiliation:
Department of Mechanical Engineering, National Cheng Kung University, Tainan 7010, Taiwan email ckchen@mail.ncku.edu.tw
*
✉ttlu@math.nsysu.edu.tw
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Abstract

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We propose a new Adomian decomposition method (ADM) using an integrating factor for the Emden–Fowler equation. With this method, we are able to solve certain Emden–Fowler equations for which the traditional ADM fails. Numerical results obtained from testing our linear and nonlinear models are far more reliable and efficient than those from existing methods. We also present a complete error analysis and a convergence criterion for this method. One drawback of the traditional ADM is that the interval of convergence of the Adomian truncated series is very small. Some techniques, such as Pade approximants, can enlarge this interval, but they are too complicated. Here, we use a continuation technique to extend our method to a larger interval.

Keywords

Adomian decompositionintegrating factorEmden–Fowler equationerror analysisconvergence

MSC classification

Primary: 65L05: Initial value problems
Secondary: 65L20: Stability and convergence of numerical methods 65L70: Error bounds
Type
Research Article
Information
The ANZIAM Journal , Volume 56 , Issue 2 , October 2014 , pp. 192 - 208
Copyright
Copyright © 2014 Australian Mathematical Society 

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