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Iterative Reproducing Kernel Method for Solving Second‐Order Integrodifferential Equations of Fredholm Type

Author

Listed:
  • Iryna Komashynska
  • Mohammed AL-Smadi

Abstract

We present an efficient iterative method for solving a class of nonlinear second‐order Fredholm integrodifferential equations associated with different boundary conditions. A simple algorithm is given to obtain the approximate solutions for this type of equations based on the reproducing kernel space method. The solution obtained by the method takes form of a convergent series with easily computable components. Furthermore, the error of the approximate solution is monotone decreasing with the increasing of nodal points. The reliability and efficiency of the proposed algorithm are demonstrated by some numerical experiments.

Suggested Citation

  • Iryna Komashynska & Mohammed AL-Smadi, 2014. "Iterative Reproducing Kernel Method for Solving Second‐Order Integrodifferential Equations of Fredholm Type," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:459509
    DOI: 10.1155/2014/459509
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    References listed on IDEAS

    as
    1. Z. Pashazadeh Atabakan & A. Kılıçman & A. Kazemi Nasab, 2012. "On Spectral Homotopy Analysis Method for Solving Linear Volterra and Fredholm Integrodifferential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Omar Abu Arqub & Mohammed Al-Smadi & Shaher Momani, 2012. "Application of Reproducing Kernel Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-16, September.
    3. Z. Pashazadeh Atabakan & A. Kılıçman & A. Kazemi Nasab, 2012. "On Spectral Homotopy Analysis Method for Solving Linear Volterra and Fredholm Integrodifferential Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-16, November.
    4. Omar Abu Arqub & Mohammed Al-Smadi & Shaher Momani, 2012. "Application of Reproducing Kernel Method for Solving Nonlinear Fredholm‐Volterra Integrodifferential Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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