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Legendre Spectral Projection Methods for Fredholm–Hammerstein Integral Equations

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Abstract

In this paper, we consider the Legendre spectral Galerkin and Legendre spectral collocation methods to approximate the solution of Hammerstein integral equation. The convergence of the approximate solutions to the actual solution is discussed and the rates of convergence are obtained. We are able to obtain similar superconvergence rates for the iterated Legendre Galerkin solution for Hammerstein integral equations with smooth kernel as in the case of piecewise polynomial based Galerkin method.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology, Kharagpur, 721 302, India

    Payel Das & Gnaneshwar Nelakanti

  2. Department of Mathematics, School of Applied Sciences, KIIT University, Bhubaneswar, 751 024, India

    Mitali Madhumita Sahani

  3. Department of Mathematics, GuangXi Teachers Education University, Nanning, 530001, People’s Republic of China

    Guangqing Long

Authors
  1. Payel Das
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  2. Mitali Madhumita Sahani
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  3. Gnaneshwar Nelakanti
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  4. Guangqing Long
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Correspondence to Payel Das.

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Das, P., Sahani, M.M., Nelakanti, G. et al. Legendre Spectral Projection Methods for Fredholm–Hammerstein Integral Equations. J Sci Comput 68, 213–230 (2016). https://doi.org/10.1007/s10915-015-0135-z

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  • DOI: https://doi.org/10.1007/s10915-015-0135-z

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