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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 K. Abbaoui and 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.

MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34B27 Green’s functions for ordinary differential equations
45G05 Singular nonlinear integral equations
65R20 Numerical methods for integral equations
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References:

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