Large interval solution of the Emden–Fowler equation using a modified Adomian decomposition method with an integrating factor

Yinwei Lin, Tzon-Tzer Lu, Cha'o-Kuang Chen

Abstract


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.

doi:10.1017/S1446181114000340

Keywords


Adomian decomposition, integrating factor, Emden–Fowler equation, error analysis, convergence



DOI: http://dx.doi.org/10.21914/anziamj.v56i0.6912



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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.