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K. E. Atkinson, “A Survey of Numerical Methods for the Solution of Fredholm Integral Equations of the Second Kind,” Society for Industrial and Applied Mathematics, Philadelphia, 1976, p. 237.

has been cited by the following article:

• TITLE: Convergence of Discrete Adomian Method for Solving a Class of Nonlinear Fredholm Integral Equations

  AUTHORS: Ibrahim Lotfy Hassan Alkalla, Reda Abdo Abd-Elmonem, Ayman Mohamed Ali Ahmed Gomaa

  KEYWORDS: Nonlinear Fredholm Integral Equations; Contraction Mapping; Adomian Decomposition Method; Quadratures Techniques

  JOURNAL NAME: Applied Mathematics, Vol.4 No.1A, January 30, 2013

  ABSTRACT: In recent papers the solution of nonlinear Fredholm integral equations was discussed using Adomian decomposition method (ADM). For case in which the integrals are analytically impossible, ADM can not be applied. In this paper a discretized version of the ADM is introduced and the proposed version will be called discrete Adomian decomposition method (DADM). An accelerated formula of Adomian polynomials is used in calculations. Based on this formula, a new convergence approach of ADM is introduced. Convergence approach is reliable enough to obtain an explicit formula for the maximum absolute truncated error of the Adomian’s series solution. Also, we prove that the solution of nonlinear Fredholm integral equation by DADM converges to ADM solution. Finally, some numerical examples were introduced.