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The decomposition method applied to systems of Fredholm integral equations of the second kind. (English) Zbl 1042.65104

The authors apply the Adomian decomposition method to systems of linear and nonlinear Fredholm integral equations of the second kind. They present convergence results and illustrate the performance of the method by means of two examples. The paper is an extension of closely related recent work by E. Babolian and J. Biazar [Far East J. Math. Sci. (FJMS) 2, 935–946 (2000; Zbl 0979.65123)] on the use of this method for systems of nonlinear Volterra integral equations.

MSC:

65R20 Numerical methods for integral equations
45F05 Systems of nonsingular linear integral equations
45G15 Systems of nonlinear integral equations

Citations:

Zbl 0979.65123
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References:

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[2] Adomian, G., Solving frontier problems of physics: the decomposition method, (1994), Kluwer · Zbl 0802.65122
[3] Cherruault, Y.; Saccomandi, G., New results for convergence of Adomian method applied to integral equations, Math. comput. modelling, 16, 2, 83-93, (1992) · Zbl 0756.65083
[4] Cherruault, Y.; Seng, V., The resolution of nonlinear integral equations of the first kind using the decomposition method of Adomian, Kybernetes, 26, 2, 198-206, (1997) · Zbl 0932.65142
[5] Babolian, E.; Biazar, J., Solution of a system of nonlinear Volterra equations by Adomian decomposition method, Far east J. math. sci., 2, 6, 935-945, (2000) · Zbl 0979.65123
[6] Babolian, E.; Biazar, J., Solution of a system of linear Volterra equations by Adomian decomposition method, Far east J. math. sci., 7, 1, 17-25, (2001) · Zbl 1012.65146
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