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Zbl 0959.65091
Deeba, Elias; Khuri, S.A.; Xie, Shishen
An algorithm for solving boundary value problems. (English)
[J] J. Comput. Phys. 159, No.2, 125-138 (2000). ISSN 0021-9991

This paper deals with nonlinear Fredholm integral equations. The decomposition method of Adomian is used. Numerical experiments are given proving the adequacy of the method. But the authors do not know recent results by {\it K. Abbaoui} and {\it Y. Cherruault} [Comput. Math. Appl. 28, No. 5, 103-109 (1994; Zbl 0809.65073); ibid. 29, No. 7, 103-108 (1995; Zbl 0832.47051)] for calculating easily, in a recurrent way, the Adomian polynomials. These results allow to decrease the calculation time. Remark that the integral representation is obtained through the Green's function when applied to boundary value problems.
[Yves Cherruault (Paris)]

MSC 2000:: *65L10 Boundary value problems for ODE (numerical methods)
34B15 Nonlinear boundary value problems of ODE
34B27 Green functions
45G05 Singular nonlinear integral equations
65R20 Integral equations (numerical methods)

Keywords: Bratu's problem; numerical experiments; nonlinear Fredholm integral equations; decomposition method of Adomian

Citations: Zbl 0809.65073; Zbl 0832.47051

Cited in: Zbl 0983.65092

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