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A New Modification of Adomian Decomposition Method for Volterra Integral Equations of the Second Kind

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  • Lie-jun Xie

Abstract

We propose a new modification of the Adomian decomposition method for Volterra integral equations of the second kind. By the Taylor expansion of the components apart from the zeroth term of the Adomian series solution, this new technology overcomes the problems arising from the previous decomposition method. The validity and applicability of the new technique are illustrated through several linear and nonlinear equations by comparing with the standard decomposition method and the modified decomposition method. The results obtained indicate that the new modification is effective and promising.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:795015
    DOI: 10.1155/2013/795015
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    References listed on IDEAS

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    1. Abdul-Majid Wazwaz, 2011. "Linear and Nonlinear Integral Equations," Springer Books, Springer, number 978-3-642-21449-3, March.
    2. Tien, Wei-Chung & Chen, Cha’o-Kuang, 2009. "Adomian decomposition method by Legendre polynomials," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2093-2101.
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