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Rationalized Haar wavelet bases to approximate solution of nonlinear Fredholm integral equations with error analysis

Author

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  • Erfanian, M.
  • Gachpazan, M.
  • Beiglo, H.

Abstract

In this article we approximate the solutions of the nonlinear Fredholm integral equations of the second kind, by the method based on using the properties of RH wavelets and matrix operator. Also, the Banach fixed point theorem guarantees the convergence of the method. Also we get an upper bound for the error. Furthermore, the order of convergence is analyzed. The algorithm to compute the solutions and some numerical examples are also illustrated. The numerical results obtained by our method have been compared with other methods.

Suggested Citation

  • Erfanian, M. & Gachpazan, M. & Beiglo, H., 2015. "Rationalized Haar wavelet bases to approximate solution of nonlinear Fredholm integral equations with error analysis," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 304-312.
    • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:304-312
    DOI: 10.1016/j.amc.2015.05.010
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    Cited by:

    1. Erfanian, Majid & Mansoori, Amin, 2019. "Solving the nonlinear integro-differential equation in complex plane with rationalized Haar wavelet," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 165(C), pages 223-237.
    2. Baghani, Omid, 2019. "A correction to “Rationalized Haar wavelet bases to approximate solution of nonlinear Fredholm integral equations with error analysis [Applied Mathematics and Computation 265 (2015) 304–312]”," Applied Mathematics and Computation, Elsevier, vol. 352(C), pages 249-257.
    3. Beiglo, H. & Gachpazan, M., 2020. "Numerical solution of nonlinear mixed Volterra-Fredholm integral equations in complex plane via PQWs," Applied Mathematics and Computation, Elsevier, vol. 369(C).

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