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Adomian decomposition method by Legendre polynomials

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  • Tien, Wei-Chung
  • Chen, Cha’o-Kuang

Abstract

In this paper, an efficient modification of the Adomian decomposition method by using Legendre polynomials is presented. Both linear and non-linear models are suited for the proposed method. Some examples here in are solved by using this method and this paper will demonstrate that the results are more reliable and efficient.

Suggested Citation

  • Tien, Wei-Chung & Chen, Cha’o-Kuang, 2009. "Adomian decomposition method by Legendre polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2093-2101.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:5:p:2093-2101
    DOI: 10.1016/j.chaos.2007.06.066
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    References listed on IDEAS

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    1. Wang, Yue-yue & Dai, Chao-qing & Wu, Lei & Zhang, Jie-fang, 2007. "Exact and numerical solitary wave solutions of generalized Zakharov equation by the Adomian decomposition method," Chaos, Solitons & Fractals, Elsevier, vol. 32(3), pages 1208-1214.
    2. Momani, Shaher & Odibat, Zaid, 2007. "Numerical comparison of methods for solving linear differential equations of fractional order," Chaos, Solitons & Fractals, Elsevier, vol. 31(5), pages 1248-1255.
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    Cited by:

    1. 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).
    2. Lie-jun Xie, 2013. "A New Modification of Adomian Decomposition Method for Volterra Integral Equations of the Second Kind," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    3. Sekson Sirisubtawee & Supaporn Kaewta, 2017. "New Modified Adomian Decomposition Recursion Schemes for Solving Certain Types of Nonlinear Fractional Two-Point Boundary Value Problems," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2017, pages 1-20, July.

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