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Reproducing Kernel Method for Solving Nonlinear Differential‐Difference Equations

Author

Listed:
  • Reza Mokhtari
  • Fereshteh Toutian Isfahani
  • Maryam Mohammadi

Abstract

On the basis of reproducing kernel Hilbert spaces theory, an iterative algorithm for solving some nonlinear differential‐difference equations (NDDEs) is presented. The analytical solution is shown in a series form in a reproducing kernel space, and the approximate solution un,m is constructed by truncating the series to m terms. The convergence of un,m to the analytical solution is also proved. Results obtained by the proposed method imply that it can be considered as a simple and accurate method for solving such differential‐difference problems.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:514103
    DOI: 10.1155/2012/514103
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    References listed on IDEAS

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    1. 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).
    2. 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.
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    Cited by:

    1. Yulan Wang & Shuai Lu & Fugui Tan & Mingjing Du & Hao Yu, 2013. "Solving a Class of Singular Fifth‐Order Boundary Value Problems Using Reproducing Kernel Hilbert Space Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. 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).

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