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

Author

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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 u(x) is represented in the form of series in the reproducing kernel space. In the mean time, the n‐term approximate solution un(x) is obtained and it is proved to converge to the exact solution u(x). 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, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:839836
    DOI: 10.1155/2012/839836
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    Cited by:

    1. Omar Abu Arqub & Ahmad El-Ajou & A. Sami Bataineh & I. Hashim, 2013. "A Representation of the Exact Solution of Generalized Lane‐Emden Equations Using a New Analytical Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. Mohammed AL-Smadi & Omar Abu Arqub & Ahmad El-Ajou, 2014. "A Numerical Iterative Method for Solving Systems of First‐Order Periodic Boundary Value Problems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    3. Banan Maayah & Samia Bushnaq & Shaher Momani & Omar Abu Arqub, 2014. "Iterative Multistep Reproducing Kernel Hilbert Space Method for Solving Strongly Nonlinear Oscillators," Advances in Mathematical Physics, John Wiley & Sons, vol. 2014(1).
    4. Li-Hong Yang & Hong-Ying Li & Jing-Ran Wang, 2013. "Solving a System of Linear Volterra Integral Equations Using the Modified Reproducing Kernel Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    5. 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).
    6. 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).

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