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A Coupled Method of Laplace Transform and Legendre Wavelets for Lane‐Emden‐Type Differential Equations

Author

Listed:
  • Fukang Yin
  • Junqiang Song
  • Fengshun Lu
  • Hongze Leng

Abstract

A coupled method of Laplace transform and Legendre wavelets is presented to obtain exact solutions of Lane‐Emden‐type equations. By employing properties of Laplace transform, a new operator is first introduced and then its Legendre wavelets operational matrix is derived to convert the Lane‐Emden equations into a system of algebraic equations. Block pulse functions are used to calculate the Legendre wavelets coefficient matrices of the nonlinear terms. The results show that the proposed method is very effective and easy to implement.

Suggested Citation

  • Fukang Yin & Junqiang Song & Fengshun Lu & Hongze Leng, 2012. "A Coupled Method of Laplace Transform and Legendre Wavelets for Lane‐Emden‐Type Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:163821
    DOI: 10.1155/2012/163821
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    References listed on IDEAS

    as
    1. Changqing Yang & Jianhua Hou, 2012. "A Numerical Method for Lane-Emden Equations Using Hybrid Functions and the Collocation Method," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-9, February.
    2. Changqing Yang & Jianhua Hou, 2012. "A Numerical Method for Lane‐Emden Equations Using Hybrid Functions and the Collocation Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    3. Abbasbandy, S., 2006. "Application of He’s homotopy perturbation method for Laplace transform," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1206-1212.
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    Cited by:

    1. B. A. Jacobs & C. Harley, 2014. "Two Hybrid Methods for Solving Two‐Dimensional Linear Time‐Fractional Partial Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Fukang Yin & Junqiang Song & Xiaoqun Cao & Fengshun Lu, 2013. "Couple of the Variational Iteration Method and Legendre Wavelets for Nonlinear Partial Differential Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).

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