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

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References

[1] 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.

[2] F. G. Tricomi, “Integral Equations,” Dover Publications Inc., New York, 1985.

[3] L. M. Delves and J. L. Mohamed, “Computational Methods for Integral Equations,” Cambridge University Press, New York, 1985. doi:10.1017/CBO9780511569609

[4] M. A. Golbluerg, “Numerical Solution of Integral Equations,” Plenum Press, New York, 1990.

[5] G. Adomian, “Solving Frontier Problems of Physics: The Decomposition Method,” Kluwer Academic Publishers, Dordrecht, 1994.

[6] A. M. Wazwaz and S. A. Khuri, “Two Methods for Solving Integral Equations,” Applied Mathematics and Computation, Vol. 77, No. 1, 1996, pp. 79-89.
doi:10.1016/0096-3003(95)00189-1

[7] A. M. Wazwaz, “A First Course in Integral Equations,” World Scientific Publishing Co., Singapore City, 1997.
doi:10.1142/3444

[8] E. Babolian, J. Biazar and A. R. Vahidi, “The Decomposition Method Applied to Systems of Fredholm Integral Equations of the Second Kind,” Applied Mathematics and Computation, Vol. 148, No. 2, 2004, pp. 443-452.
doi:10.1016/S0096-3003(02)00859-7

[9] A. M. Wazwaz, “A Comparison Study between the Modified Decomposition Method and the Traditional Methods for Solving Nonlinear Integral Equations,” Applied Mathematics and Computation, Vol. 181, No. 2, 2006, pp. 1703-1712. doi:10.1016/j.amc.2006.03.023

[10] Y. Cherruault, G. Adomian, K. Abbaoui and R. Rach, “Further Remarks on Convergence of Decomposition Method,” International Journal of Bio-Medical Computing, Vol. 38, No. 1, 1995, pp. 89-93.
doi:10.1016/0020-7101(94)01042-Y

[11] I. L. El-kalla, “Convergence of Adomian’s Method Applied to a Class of Volterra Type Integro-Differential Equations,” International Journal of Differential Equations and Applications, Vol. 10, No. 2, 2005, pp. 225-234.

[12] I. L. El-kalla, “Error Analysis of Adomian Series Solution to a Class of Nonlinear Differential Equations,” Applied Mathematics E-Notes, Vol. 7, 2007, pp. 214-221.

[13] I. L. El-Kalla, “Error Estimate of the Series Solution to a Class of Nonlinear Fractional Differential Equations,” Communications in Nonlinear Science and Numerical Simulation, Vol. 16, No. 3, 2011, pp. 1408-1413.
doi:10.1016/j.cnsns.2010.05.030

[14] E. A. Az-Zo’bi and K. Al-Khaled, “A New Convergence Proof of the Adomian Decomposition Method for a Mixed Hyperbolic Elliptic System of Conservation Laws,” Applied Mathematics and Computation, Vol. 217, No. 8, 2010, pp. 4248-4256.

[15] E. Babolian and A. Davari, “Numerical Implementation of Adomain Decomposition Method,” Applied Mathematics and Computation, Vol. 153, No. 1, 2004, pp. 301-305. doi:10.1016/S0096-3003(03)00646-5

[16] A. J. Jerri, “Introduction to Integral Equations with Applications,” John Wiley & Sons Inc., New York, 1999.

[17] J. Stoer and R. Bulirsch, “Introduction to Numerical Analysis,” 3rd Edition, Springer-Verlag, Berlin, Heidelberg, New York, 2002.

[18] K. E. Atkinson, “The Numerical Solution of Integral Equations of the Second Kind,” Cambridge University Press, New York, 1997.
doi:10.1017/CBO9780511626340

[19] K. Abbaoui and Y. Cherruault, “New Ideas for Proving Convergence of Decomposition Methods,” Computers & Mathematics with Applications, Vol. 29, No. 7, 1995, pp. 103-108. doi:10.1016/0898-1221(95)00022-Q

[20] M. M. Hosseini and H. Nasabzadeh, “On the Convergence of Adomian Decomposition Method,” Applied Mathematics and Computation, Vol. 182, No. 1, 2006, pp. 536-543. doi:10.1016/j.amc.2006.04.015

[21] K. Abbaoui and Y. Cherruault, “Convergence of Adomian’s Method Applied to Differential Equations,” Computers & Mathematics with Applications, Vol. 28, No. 5, 1994, pp. 103-109.
doi:10.1016/0898-1221(94)00144-8

[22] R. Rajaram and M. Najafi, “Analytical Treatment and Convergence of the Adomian Decomposition Method for a System of Coupled Damped Wave Equations,” Applied Mathematics and Computation, Vol. 212, No. 1, 2009, pp. 72-81. doi:10.1016/j.amc.2009.02.006

[23] E. Kreyszig, “Introductory Functional Analysis with Applications,” John Wiley & Sons Inc., New York, 1978.