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Application of Reproducing Kernel Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations

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  • Omar Abu Arqub
  • Mohammed Al-Smadi
  • Shaher Momani

Abstract

This paper investigates the numerical solution of nonlinear Fredholm-Volterra integro-differential equations using reproducing kernel Hilbert space method. The solution ð ‘¢ ( ð ‘¥ ) is represented in the form of series in the reproducing kernel space. In the mean time, the n -term approximate solution ð ‘¢ ð ‘› ( ð ‘¥ ) is obtained and it is proved to converge to the exact solution ð ‘¢ ( ð ‘¥ ) . Furthermore, the proposed method has an advantage that it is possible to pick any point in the interval of integration and as well the approximate solution and its derivative will be applicable. Numerical examples are included to demonstrate the accuracy and applicability of the presented technique. The results reveal that the method is very effective and simple.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnlaaa:839836
    DOI: 10.1155/2012/839836
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    Cited by:

    1. Alvandi, Azizallah & Paripour, Mahmoud, 2019. "The combined reproducing kernel method and Taylor series for handling nonlinear Volterra integro-differential equations with derivative type kernel," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 151-160.

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