Picard and adomian methods for quadratic integral equation

被引：36

作者：

El-Sayed A.M.A. ^{[1
]}

Hashem H.H.G. ^{[2
]}

Ziada E.A.A. ^{[2
]}

机构：

[1] Faculty of Science, Alexandria University, Alexandria

[2] Faculty of Engineering, Mansoura University, Mansoura

来源：

Computational and Applied Mathematics | 2010年 / 29卷 / 03期

关键词：

Adomian method; Continuous unique solution; Convergence analysis; Error analysis; Picard method; Quadratic integral equation;

D O I：

10.1590/S1807-03022010000300007

中图分类号：

学科分类号：

摘要：

We are concerning with two analytical methods; the classical method of successive approximations (Picard method) [14] which consists the construction of a sequence of functions such that the limit of this sequence of functions in the sense of uniform convergence is the solution of a quadratic integral equation, and Adomian method which gives the solution as a series see ([1-6], [12] and [13]). The existence and uniqueness of the solution and the convergence will be discussed for each method. © 2010 SBMAC.

引用

页码：447 / 463

页数：16

共 22 条

[1]

Adomian G., Stochastic System, (1983)

[2]

Adomian G., Nonlinear Stochastic Operator Equations, (1986)

[3]

Adomian G., Nonlinear Stochastic Systems: Theory and Applications to Physics, (1989)

[4]

Adomian G., Rach R., Mayer R., Modified decomposition, J. Appl. Math. Comput., 23, pp. 17-23, (1992)

[5]

Abbaoui K., Cherruault Y., Convergence of Adomian's method Applied to Differential Equations, Computers Math. Applic., 28, pp. 103-109, (1994)

[6]

Adomian G., Solving Frontier Problems of Physics: The Decomposition Method, (1995)

[7]

Banas J., Lecko M., El-Sayed W.G., Existence Theorems of Some Quadratic Integral Equation, J. Math. Anal. Appl., 227, pp. 276-279, (1998)

[8]

Banas J., Martinon A., Monotonic Solutions of a quadratic Integral Equation of Volterra Type, Comput. Math. Appl., 47, pp. 271-279, (2004)

[9]

Banas J., Caballero J., Rocha J., Sadarangani K., Monotonic Solutions of a Class of Quadratic Integral Equations of Volterra Type, Computers and Mathematics with Applications, 49, pp. 943-952, (2005)

[10]

Banas J., Rocha Martin J., Sadarangani K., On the solution of a quadratic integral equation of Hammerstein type, Mathematical and Computer Modelling, 43, pp. 97-104, (2006)

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