Solving the Systems of Equations of Lane-Emden Type by Differential Transform Method Coupled with Adomian Polynomials

Lie-jun Xie, Cai-lian Zhou and Song Xu
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Lie-jun Xie: School of Mathematics and Statistics, Ningbo University, No. 818 Fenghua Road, Ningbo 315211, Zhejiang, China
Cai-lian Zhou: School of Mathematics and Statistics, Ningbo University, No. 818 Fenghua Road, Ningbo 315211, Zhejiang, China
Song Xu: School of Mathematics and Statistics, Ningbo University, No. 818 Fenghua Road, Ningbo 315211, Zhejiang, China

Mathematics, 2019, vol. 7, issue 4, 1-16

Abstract: In this work, we applied the improved differential transform method to find the solutions of the systems of equations of Lane-Emden type arising in various physical models. With our proposed scheme, the desired solutions take the form of a convergent series with easily computable components. The results disclosing the relation between the differential transforms of multi-variables and the corresponding Adomian polynomials are proven. One can see that both the differential transforms and the Adomian polynomials of those nonlinearities have the same mathematical structure merely with constants instead of variable components. By using this relation, we computed the differential transforms of nonlinear functions given in the systems. The validity and applicability of the proposed method are illustrated through several homogeneous and nonhomogeneous nonlinear systems.

Keywords: systems of equations of Lane-Emden type; differential transform method; Adomian polynomials; singular behavior (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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