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Solving a Class of Singularly Perturbed Partial Differential Equation by Using the Perturbation Method and Reproducing Kernel Method

Author

Listed:
  • Yu-Lan Wang
  • Hao Yu
  • Fu-Gui Tan
  • Shanshan Qu

Abstract

We give the analytical solution and the series expansion solution of a class of singularly perturbed partial differential equation (SPPDE) by combining traditional perturbation method (PM) and reproducing kernel method (RKM). The numerical example is studied to demonstrate the accuracy of the present method. Results obtained by the method indicate the method is simple and effective.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:615840
    DOI: 10.1155/2014/615840
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    References listed on IDEAS

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    1. Yuefeng Han & Xinguang Zhang & Lishan Liu & Yonghong Wu, 2012. "Multiple Positive Solutions of Singular Nonlinear Sturm‐Liouville Problems with Carathéodory Perturbed Term," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Yuefeng Han & Xinguang Zhang & Lishan Liu & Yonghong Wu, 2012. "Multiple Positive Solutions of Singular Nonlinear Sturm-Liouville Problems with Carathéodory Perturbed Term," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-23, January.
    3. Reza Mokhtari & Fereshteh Toutian Isfahani & Maryam Mohammadi, 2012. "Reproducing Kernel Method for Solving Nonlinear Differential‐Difference Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. Chang Phang & Yonghong Wu & Benchawan Wiwatanapataphee, 2013. "Computation of the Domain of Attraction for Suboptimal Immunity Epidemic Models Using the Maximal Lyapunov Function Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. F. Z. Geng & X. M. Li, 2012. "A New Method for Riccati Differential Equations Based on Reproducing Kernel and Quasilinearization Methods," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    6. Reza Mokhtari & Fereshteh Toutian Isfahani & Maryam Mohammadi, 2012. "Reproducing Kernel Method for Solving Nonlinear Differential-Difference Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-10, July.
    7. Samia Bushnaq & Banan Maayah & Shaher Momani & Ahmed Alsaedi, 2014. "A Reproducing Kernel Hilbert Space Method for Solving Systems of Fractional Integrodifferential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    8. 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).
    9. 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.
    10. Mustafa Inc & Ali Akgül, 2014. "Numerical Solution of Seventh-Order Boundary Value Problems by a Novel Method," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, March.
    11. F. Z. Geng & S. P. Qian, 2014. "Solving Singularly Perturbed Multipantograph Delay Equations Based on the Reproducing Kernel Method," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, February.
    12. X. Y. Li & B. Y. Wu & R. T. Wang, 2014. "Reproducing Kernel Method for Fractional Riccati Differential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    13. Samia Bushnaq & Banan Maayah & Shaher Momani & Ahmed Alsaedi, 2014. "A Reproducing Kernel Hilbert Space Method for Solving Systems of Fractional Integrodifferential Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, March.
    14. Mustafa Inc & Ali Akgül, 2014. "Numerical Solution of Seventh‐Order Boundary Value Problems by a Novel Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    15. Chang Phang & Yonghong Wu & Benchawan Wiwatanapataphee, 2013. "Computation of the Domain of Attraction for Suboptimal Immunity Epidemic Models Using the Maximal Lyapunov Function Method," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, February.
    16. X. Y. Li & B. Y. Wu & R. T. Wang, 2014. "Reproducing Kernel Method for Fractional Riccati Differential Equations," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, April.
    17. F. Z. Geng & X. M. Li, 2012. "A New Method for Riccati Differential Equations Based on Reproducing Kernel and Quasilinearization Methods," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-8, March.
    18. 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).
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