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**The Appearance of Noise Terms in Modified Adomian Decomposition Method for Quadratic Integral Equations** ()

In this paper, we apply the modified Adomian Decomposition Method to get the numerical solutions of Quadratic integral equations. The appearance of noise terms in Decomposition Method was investigated. The method was described along with several examples.

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H. Bakodah, "The Appearance of Noise Terms in Modified Adomian Decomposition Method for Quadratic Integral Equations,"

*American Journal of Computational Mathematics*, Vol. 2 No. 2, 2012, pp. 125-129. doi: 10.4236/ajcm.2012.22017.Conflicts of Interest

The authors declare no conflicts of interest.

[1] | J. Appell, “On the Solvability of Nonlinear Non-Compact Problems in Function Spaces with Applications to Integral and Differential Equations,” Bollettino della Unione Matematica Italiana, Vol. 6, No. 1B, 1982, pp. 1161-1177. |

[2] | J. Banas and K. Goebel, “Measures of Non-Compactness in Banach Spaces,” Dekker, New York, 1980. |

[3] | L. W. Busbridge, “The Mathematics of Radiative Transfer,” Cambridge University Press, Cambridge, 1960. |

[4] | J. Banas, J. Rocha Mortin and K. Sadarangani, “On the Solution of a Quadratic Integral Equation of Hammerstein Type,” Mathematical and Computer Modelling, Vol. 43, No. 1-2, 2006, pp. 97-104. doi:10.1016/j.mcm.2005.04.017 |

[5] | W. G. El-Sayed and B. Rzepka, “Non Decreasing Solutions of a Quadratic Integral Equations of Uryshon Type,” Computers & Mathematics with Applications, Vol. 51, No. 6-7, 2006, pp. 1065-1074. doi:10.1016/j.camwa.2005.08.033 |

[6] | A. M. A. El-Sayed and H. H. G. Hashem, “Solvability of Nonlinear Hammerstein Quadratic Integral Equations,” Journal of Nonlinear Sciences and Its Applications, Vol. 2, No. 3, 2009, pp. 152-160. |

[7] | I. K. Argyros, “Quadratic Equation and Applications to Chandrasckar’s and Related Equations,” Bulletin of the Australian Mathematical Society, Vol. 32, No. 2, 1985, pp. 275-292. doi:10.1017/S0004972700009953 |

[8] | J. Caballero, B. Lopez and K. Sadaramgani, “Existence of Non Decreasing and Continuous Solutions for a Nonlinear Integral Equation with Supremum in the Kernel,” Zeitschrift für Analysis und ihre Anwendungen, Vol. 26, No. 2, 2007, pp. 195-205. doi:10.4171/ZAA/1318 |

[9] | M. A. Darwish, “On Solvability of Some Quadratic Functional Integral Equations in Banach Algebra,” Communications in Applied Analysis, Vol. 11, 2007, pp. 441-450. |

[10] | A. M. El-Sayed, H. G. Hashem and E. A. Ziada, “Picard and Adomian Methods for Quadratic Integral Equation,” Computational & Applied Mathematics, Vol. 29, No. 3, 2010, pp. 447-463. doi:10.1590/S1807-03022010000300007 |

[11] | G. Adomian, R. C. Rach and R. E. Meyers, “An Efficient Methodology for Physical Sciences,” Kybernetes, Vol. 20, No. 7, 1991, pp. 24-34. doi:10.1108/eb005909 |

[12] | G. Adomian, “A Review of Decomposition Method and Some Recent Result for Nonlinear Equations,” Mathematical and Computer Modelling, Vol. 13, No. 7, 1992, pp. 17-43. doi:10.1016/0895-7177(90)90125-7 |

[13] | G. Adomian, “Solving Frontier Problems of Physics: The Decomposition Method,” Springer, Berlin, 1994. |

[14] | G. Adomian, “Nonlinear Stochastic Systems: Theory and Applications to Physics,” Springer, Berlin, 1989. |

[15] | A. Wazwaz, “A Reliable Modification of Adomian Decomposition Method,” Applied Mathematics and Computation, Vol. 92, No. 1,1998, pp. 1-7. doi:10.1016/S0096-3003(97)10037-6 |

[16] | G. Adomian and R. Rach, “Noise Terms in Decomposition Series Solution,” Computers & Mathematics with Applications, Vol. 24, No. 11, 1992, pp. 61-64. doi:10.1016/0898-1221(92)90031-C |

[17] | A. Wazwaz, “Neessary Conditions for the Appearance of Noise Terms in De-composition Solution Series,” Applied Mathematics and Computation, Vol. 81, No. 2-3, 1997, pp. 265-274. doi:10.1016/S0096-3003(95)00327-4 |

[18] | A. Wazwaz, “The Existence of Noise Terms for Systems of Inhomogeneous Differential and Integral Equations,” Applied Mathematics and Computation, Vol. 146, No. 1, 2003, pp. 81-92. doi:10.1016/S0096-3003(02)00527-1 |

[19] | A. Wazwaz and S. M. El-Syed, “A New Modification of the Adomian Decomposition Method for Linear and Non- linear Operators,” Applied Mathematics and Computation, Vol. 122, No. 3, 2001, pp. 393-405. doi:10.1016/S0096-3003(00)00060-6 |

[20] | J. Banas and A. Martinon, “Monotonic Solutions of a Quadratic Integral Equations of Volterra Type,” Computers & Mathematics with Applications, Vol. 47, No. 2-3, 2004, pp. 271-279. doi:10.1016/S0898-1221(04)90024-7 |

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