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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Lie-jun Xie & Cai-lian Zhou & Song Xu, 2019. "Solving the Systems of Equations of Lane-Emden Type by Differential Transform Method Coupled with Adomian Polynomials," Mathematics, MDPI, vol. 7(4), pages 1-16, April.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:377-:d:225930
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    References listed on IDEAS

    as
    1. Mossa Al-sawalha, M. & Noorani, M.S.M., 2009. "A numeric–analytic method for approximating the chaotic Chen system," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1784-1791.
    2. S. Gh. Hosseini & S. Abbasbandy, 2015. "Solution of Lane-Emden Type Equations by Combination of the Spectral Method and Adomian Decomposition Method," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-10, April.
    3. Robert Dalmasso, 2005. "Existence and uniqueness of solutions for a semilinear elliptic system," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2005, pages 1-17, January.
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