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“School of Mathematics”

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Paper   IPM / M / 8894
School of Mathematics
  Title:   Error estimate in the Sinc collocation method for Volterra-Fredholm integral equations based on de transformation
  Author(s):  M. Hadizadeh (Joint with Gh. Kazemi Gelian)
  Status:   Published
  Journal: Electron. Trans. Numer. Anal.
  Vol.:  30
  Year:  2008
  Pages:   75-87
  Supported by:  IPM
  Abstract:
We present a method and experimental results for approximate solution of nonlinear VoltelTa-Fredholm integral equations by double exponential (DE) transformation based on the sine collocation method. It is well known that by applying DE transformation the rate of convergence O(exp( −cN/log N)) is attained. where N is a parameter representing the number of terms of the sine expansion. The purpose of this paper is to develop the work carried out in 2005 by Muhammad et al. [J. Comput. Appl. Math., 177 (2005), pp. 269-286], for the numerical solution of two dimensional nonlinear Volterra-Fredholm integral equations. We design a numerical scheme for these equations based on the sine collocation method incorporated with the DE transfonnation. A new error estimation by truncation is also obtained which is shown to have an exponential order of convergence as in Muhammad et al. (op. cit.). Finally, the reliability and efficiency of the proposed scheme are demonstrated by some numerical experiments.

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