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On Bernstein Polynomials Method to the System of Abel Integral Equations

Author

Listed:
  • A. Jafarian
  • S. Measoomy Nia
  • Alireza K. Golmankhaneh
  • D. Baleanu

Abstract

This paper deals with a new implementation of the Bernstein polynomials method to the numerical solution of a special kind of singular system. For this aim, first the truncated Bernstein series polynomials of the solution functions are substituted in the given problem. Using some properties of these polynomials, the solution of the problem is reduced to solve a linear system of algebraic equations. In order to confirm the reliability and accuracy of the proposed method, some weakly Abel integral equations systems with comparisons are solved in detail as numerical examples.

Suggested Citation

  • A. Jafarian & S. Measoomy Nia & Alireza K. Golmankhaneh & D. Baleanu, 2014. "On Bernstein Polynomials Method to the System of Abel Integral Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:796286
    DOI: 10.1155/2014/796286
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    References listed on IDEAS

    as
    1. Dumitru Baleanu & Mohsen Alipour & Hossein Jafari, 2013. "The Bernstein Operational Matrices for Solving the Fractional Quadratic Riccati Differential Equations with the Riemann-Liouville Derivative," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-7, June.
    2. Abdul-Majid Wazwaz, 2011. "Linear and Nonlinear Integral Equations," Springer Books, Springer, number 978-3-642-21449-3, October.
    3. Dumitru Baleanu & Mohsen Alipour & Hossein Jafari, 2013. "The Bernstein Operational Matrices for Solving the Fractional Quadratic Riccati Differential Equations with the Riemann‐Liouville Derivative," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    Full references (including those not matched with items on IDEAS)

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