IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v7y2019i4p377-d225930.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/7/4/377/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/7/4/377/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.

      Corrections

      All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:7:y:2019:i:4:p:377-:d:225930. See general information about how to correct material in RePEc.

      If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

      If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

      If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

      For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

      Please note that corrections may take a couple of weeks to filter through the various RePEc services.

      IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.