Abstract
This paper deals with two problems. The first of them is a boundary value problem for a nonlinear singular perturbed system of differential-algebraic equations having several solutions that can be applied to the simulation of the creep process of metal constructions. The second one is a practical problem of defining steady state stress in rotating solid disks at a constant temperature. The technique of neural network modeling is applied to solving these problems. The neural network approximate solutions agree well with the results of other authors obtained by the traditional methods.
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Achnowledgements
The work was supported by the Russian Foundation for Basic Research, project numbers 16-08-00943, 14-01-00660, and 14-01-00733.
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Budkina, E.M., Kuznetsov, E.B., Lazovskaya, T.V., Leonov, S.S., Tarkhov, D.A., Vasilyev, A.N. (2016). Neural Network Technique in Boundary Value Problems for Ordinary Differential Equations. In: Cheng, L., Liu, Q., Ronzhin, A. (eds) Advances in Neural Networks – ISNN 2016. ISNN 2016. Lecture Notes in Computer Science(), vol 9719. Springer, Cham. https://doi.org/10.1007/978-3-319-40663-3_32
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DOI: https://doi.org/10.1007/978-3-319-40663-3_32
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