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An algorithm for solving boundary value problems. (English) Zbl 0959.65091
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.

65L10Boundary value problems for ODE (numerical methods)
34B15Nonlinear boundary value problems for ODE
34B27Green functions
45G05Singular nonlinear integral equations
65R20Integral equations (numerical methods)
Full Text: DOI
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