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Volume 7
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10.3390/math7040377
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Article

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

by
Lie-jun Xie
*,
Cai-lian Zhou
and
Song Xu
School of Mathematics and Statistics, Ningbo University, No. 818 Fenghua Road, Ningbo 315211, Zhejiang, China
*
Author to whom correspondence should be addressed.
Mathematics 2019, 7(4), 377; https://doi.org/10.3390/math7040377
Submission received: 3 February 2019 / Revised: 14 April 2019 / Accepted: 23 April 2019 / Published: 25 April 2019
(This article belongs to the Section E1: Mathematics and Computer Science)
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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 systems of equations of Lane-Emden type; differential transform method; Adomian polynomials; singular behavior

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MDPI and ACS Style

Xie, L.-j.; Zhou, C.-l.; Xu, S. Solving the Systems of Equations of Lane-Emden Type by Differential Transform Method Coupled with Adomian Polynomials. Mathematics 2019, 7, 377. https://doi.org/10.3390/math7040377

AMA Style

Xie L-j, Zhou C-l, Xu S. Solving the Systems of Equations of Lane-Emden Type by Differential Transform Method Coupled with Adomian Polynomials. Mathematics. 2019; 7(4):377. https://doi.org/10.3390/math7040377

Chicago/Turabian Style

Xie, Lie-jun, Cai-lian Zhou, and Song Xu. 2019. "Solving the Systems of Equations of Lane-Emden Type by Differential Transform Method Coupled with Adomian Polynomials" Mathematics 7, no. 4: 377. https://doi.org/10.3390/math7040377

APA Style

Xie, L.-j., Zhou, C.-l., & Xu, S. (2019). Solving the Systems of Equations of Lane-Emden Type by Differential Transform Method Coupled with Adomian Polynomials. Mathematics, 7(4), 377. https://doi.org/10.3390/math7040377

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