Research ArticleOpen AccessGoogle Scholar indexed
The Appearance of Noise Terms in Modified Adomian Decomposition Method for Quadratic Integral Equations
Department of Mathematics, Sciences Faculty for Girls, King Abdulaziz University, Jeddah, Saudi Arabia
- 1 Department of Mathematics, Sciences Faculty for Girls, King Abdulaziz University, Jeddah, Saudi Arabia
American Journal of Computational Mathematics·Volume 02 (2012)·Pages 125–129·Published 21 June 2012·DOI10.4236/ajcm.2012.22017
Copy link · social · email
Abstract
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.
KeywordsModified Adomian Decomposition methodQuadratic integral equationThe noise Terms
- 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.
- J. Banas and K. Goebel, “Measures of Non-Compactness in Banach Spaces,” Dekker, New York, 1980.
- L. W. Busbridge, “The Mathematics of Radiative Transfer,” Cambridge University Press, Cambridge, 1960.
- 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
- 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
- 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.
- 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
- 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
- M. A. Darwish, “On Solvability of Some Quadratic Functional Integral Equations in Banach Algebra,” Communications in Applied Analysis, Vol. 11, 2007, pp. 441-450.
- 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
- 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
- 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
- G. Adomian, “Solving Frontier Problems of Physics: The Decomposition Method,” Springer, Berlin, 1994.