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Theory and computation in singular boundary value problems

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  • Al-Khaled, Kamel

Abstract

This paper applies the Sinc-Galerkin method and He’s homotopy perturbation method to search for approximate solutions of a certain class of singular two-point boundary value problems. The sinc method converges exponentially to the exact solution. A new iterative scheme based on He’s homotopy perturbation method is proposed for the discussed problem. A numerical example is given to demonstrate the computational efficiency of the two methods.

Suggested Citation

  • Al-Khaled, Kamel, 2007. "Theory and computation in singular boundary value problems," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 678-684.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:2:p:678-684
    DOI: 10.1016/j.chaos.2006.01.047
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    References listed on IDEAS

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    1. Vinagre, Sandra & Severino, Ricardo & Ramos, J. Sousa, 2005. "Topological invariants in nonlinear boundary value problems," Chaos, Solitons & Fractals, Elsevier, vol. 25(1), pages 65-78.
    2. He, Ji-Huan, 2005. "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 695-700.
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    Cited by:

    1. Ramos, J.I., 2008. "Series approach to the Lane–Emden equation and comparison with the homotopy perturbation method," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 400-408.
    2. Ramos, J.I., 2009. "Piecewise-adaptive decomposition methods," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1623-1636.

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