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Hybrid Bernstein Block‐Pulse Functions Method for Second Kind Integral Equations with Convergence Analysis

Author

Listed:
  • Mohsen Alipour
  • Dumitru Baleanu
  • Fereshteh Babaei

Abstract

We introduce a new combination of Bernstein polynomials (BPs) and Block‐Pulse functions (BPFs) on the interval [0, 1]. These functions are suitable for finding an approximate solution of the second kind integral equation. We call this method Hybrid Bernstein Block‐Pulse Functions Method (HBBPFM). This method is very simple such that an integral equation is reduced to a system of linear equations. On the other hand, convergence analysis for this method is discussed. The method is computationally very simple and attractive so that numerical examples illustrate the efficiency and accuracy of this method.

Suggested Citation

  • Mohsen Alipour & Dumitru Baleanu & Fereshteh Babaei, 2014. "Hybrid Bernstein Block‐Pulse Functions Method for Second Kind Integral Equations with Convergence Analysis," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:623763
    DOI: 10.1155/2014/623763
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    References listed on IDEAS

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    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. 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).
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