Convergence of Discrete Adomian Method for Solving a Class of Nonlinear Fredholm Integral Equations ()

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

Mathematics and Engineering Physics Department, Faculty of Engineering, Mansoura University, Mansoura, Egypt.

**DOI: **10.4236/am.2013.41A033
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Mathematics and Engineering Physics Department, Faculty of Engineering, Mansoura University, Mansoura, Egypt.

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.

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I. Alkalla, R. Abd-Elmonem and A. Gomaa, "Convergence of Discrete Adomian Method for Solving a Class of Nonlinear Fredholm Integral Equations," *Applied Mathematics*, Vol. 4 No. 1A, 2013, pp. 217-222. doi: 10.4236/am.2013.41A033.

Conflicts of Interest

The authors declare no conflicts of interest.

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