Optical Memory and Neural Networks

, Volume 26, Issue 2, pp 96–109 | Cite as

Neural network approach to intricate problems solving for ordinary differential equations

  • E. M. Budkina
  • E. B. Kuznetsov
  • T. V. Lazovskaya
  • D. A. Tarkhov
  • T. A. Shemyakina
  • A. N. Vasilyev
Article
  • 25 Downloads

Abstract

We consider the problems arising in the construction of the solutions of singularly perturbed differential equations. Usually, the decision of such problems by standard methods encounters significant difficulties of various kinds. The use of a common neural network approach is demonstrated in three model problems for ordinary differential equations. The conducted computational experiments confirm the effectiveness of this approach.

Keywords

neural networks ordinary differential equations 

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Copyright information

© Allerton Press, Inc. 2017

Authors and Affiliations

  • E. M. Budkina
    • 1
  • E. B. Kuznetsov
    • 1
  • T. V. Lazovskaya
    • 2
  • D. A. Tarkhov
    • 3
  • T. A. Shemyakina
    • 3
  • A. N. Vasilyev
    • 3
  1. 1.Moscow Aviation InstituteMoscowRussia
  2. 2.Computer Center of the FEB RASKhabarovskRussia
  3. 3.Peter the Great Saint-Petersburg Politechnical UniversitySt. PetersburgRussia

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