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New Modified Adomian Decomposition Recursion Schemes for Solving Certain Types of Nonlinear Fractional Two-Point Boundary Value Problems

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  • Sekson Sirisubtawee
  • Supaporn Kaewta

Abstract

We apply new modified recursion schemes obtained by the Adomian decomposition method (ADM) to analytically solve specific types of two-point boundary value problems for nonlinear fractional order ordinary and partial differential equations. The new modified recursion schemes, which sometimes utilize the technique of Duan’s convergence parameter, are derived using the Duan-Rach modified ADM. The Duan-Rach modified ADM employs all of the given boundary conditions to compute the remaining unknown constants of integration, which are then embedded in the integral solution form before constructing recursion schemes for the solution components. New modified recursion schemes obtained by the method are generated in order to analytically solve nonlinear fractional order boundary value problems with a variety of two-point boundary conditions such as Robin and separated boundary conditions. Some numerical examples of such problems are demonstrated graphically. In addition, the maximal errors or the error remainder functions of each problem are calculated.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jijmms:5742965
    DOI: 10.1155/2017/5742965
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    References listed on IDEAS

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    1. Tien, Wei-Chung & Chen, Cha’o-Kuang, 2009. "Adomian decomposition method by Legendre polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2093-2101.
    2. Hashim, I. & Noorani, M.S.M. & Ahmad, R. & Bakar, S.A. & Ismail, E.S. & Zakaria, A.M., 2006. "Accuracy of the Adomian decomposition method applied to the Lorenz system," Chaos, Solitons & Fractals, Elsevier, vol. 28(5), pages 1149-1158.
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