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Solving Singularly Perturbed Multipantograph Delay Equations Based on the Reproducing Kernel Method

Author

Listed:
  • F. Z. Geng
  • S. P. Qian

Abstract

A numerical method is presented for solving the singularly perturbed multipantograph delay equations with a boundary layer at one end point. The original problem is reduced to boundary layer and regular domain problems. The regular domain problem is solved by combining the asymptotic expansion and the reproducing kernel method (RKM). The boundary layer problem is treated by the method of scaling and the RKM. Two numerical examples are provided to illustrate the effectiveness of the present method. The results from the numerical example show that the present method can provide very accurate analytical approximate solutions.

Suggested Citation

  • F. Z. Geng & S. P. Qian, 2014. "Solving Singularly Perturbed Multipantograph Delay Equations Based on the Reproducing Kernel Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:794716
    DOI: 10.1155/2014/794716
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    References listed on IDEAS

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    1. Mustafa Inc & Ali Akgül & Adem Kiliçman, 2013. "A Novel Method for Solving KdV Equation Based on Reproducing Kernel Hilbert Space Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Mustafa Inc & Ali Akgül & Adem Kiliçman, 2013. "A Novel Method for Solving KdV Equation Based on Reproducing Kernel Hilbert Space Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, February.
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    Cited by:

    1. Yu-Lan Wang & Hao Yu & Fu-Gui Tan & Shanshan Qu, 2014. "Solving a Class of Singularly Perturbed Partial Differential Equation by Using the Perturbation Method and Reproducing Kernel Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. Yulan Wang & Hao Yu & Fugui Tan & Shuguang Li, 2014. "Using an Effective Numerical Method for Solving a Class of Lane‐Emden Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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