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Neural-Network Based Physical Fields Modeling Techniques

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Computer Science – Theory and Applications (CSR 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3967))

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Abstract

The possibility of solving elliptic and parabolic partial differential equations by using cellular neural networks with specific structure is investigated. The method of solving varialble coefficients parabolic PDEs is proposed. Issues of cellular neural network stability are examined.

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References

  1. Meade Jr., A.J., Fernandez, A.A.: The numerical solution of linear ordinary differential equations by feedforward neural networks. Mathematical Computer Modeling 19(12), 1–25 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  2. Meade Jr., A.J., Fernandez, A.A.: Solution of Nonlinear Ordinary Differential Equations by Feedforward Neural networks. Mathematical Computer Modeling 20(9), 19–44 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  3. Lee, H., Kang, I.: Neural algorithms for solving differential equations. Journal of Computational Physics 91, 110–117 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  4. Wang, L., Mendel, J.M.: Structured trainable networks for matrix algebra. IEEE Int. Joint Conference on Neural Networks 2, 125–128 (1990)

    Google Scholar 

  5. Lagaris, I.E., Likas, A., Fotiadis, D.I.: Artificial Neural Networks for Solving Ordinary and Partial Differential Equations. IEEE Trans. on Neural Networks 4, 987–1000 (1998)

    Article  Google Scholar 

  6. Fortuna, L., Arena, P., Balya, D., Zarandy, A.: Cellular Neural Networks: A Paradigm for Nonlinear Spatio-Temporal Processing. Circuits and Systems Magazine, IEEE 1(4), 6–21 (2001)

    Article  Google Scholar 

  7. Rekeczky, C., Szatmari, I., Foldesy, P., Roska, T.: Analogic Cellular PDE Machines. Analogical and Neural Computing Systems Laboratory. Computer and Automation Research Institute. Hungarian Academy of Sciences, Budapest, Hungary. Tech. Report, pp. 1–6 (2004)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Belgorod Shukhov State Technological University, Russia

    Konstantin Bournayev

Authors
  1. Konstantin Bournayev
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Editor information

Editors and Affiliations

  1. IRMAR, Université de Rennes, Campus de Beaulieu, 35042, Rennes Cedex, France

    Dima Grigoriev

  2. Intel Corporation, JF1-13, 2111 NE 25th Avenue, 97124, Hillsboro, OR, USA

    John Harrison

  3. Steklov Institute of Mathematics at St. Petersburg, 27 Fontanka, St., 191023, Petersburg, Russia

    Edward A. Hirsch

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© 2006 Springer-Verlag Berlin Heidelberg

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Bournayev, K. (2006). Neural-Network Based Physical Fields Modeling Techniques. In: Grigoriev, D., Harrison, J., Hirsch, E.A. (eds) Computer Science – Theory and Applications. CSR 2006. Lecture Notes in Computer Science, vol 3967. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11753728_40

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  • DOI: https://doi.org/10.1007/11753728_40

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-34166-6

  • Online ISBN: 978-3-540-34168-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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