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Coupled differential equations and coupled boundary conditions. (English) Zbl 0579.60057
This paper and two others by the same authors [see the following two entries; Zbl 0579.60058 and Zbl 0579.60059] are devoted to applications of the first author’s decomposition method [Stochastic systems. (1983; Zbl 0523.60056)]. In the first paper it is shown that this method yields highly accurate approximations of only a few terms when applied to coupled boundary conditions. In the second paper the technique is applied to the equation \(x=k+e^{-x}\), \(k>0\), while in the third differential equations involving the term \(y^{-m}\), where m is a positive integer, are considered.
Reviewer: A.Dale

MSC:
60H25 Random operators and equations (aspects of stochastic analysis)
34F05 Ordinary differential equations and systems with randomness
93E99 Stochastic systems and control
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References:
[1] Adomian, G., Stochastic systems, (1983), Academic Press New York · Zbl 0504.60066
[2] {\scG. Adomian}, “Nonlinear Stochastic Operator Equations,” in press. · Zbl 0609.60072
[3] {\scG. Adomian}, “Applications of Stochastic Systems Theory to Physics and Engineering,” in press. · Zbl 0659.93003
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