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Nonclassical Hamilton’s Actions and the Numerical Performance of Variational Methods for Some Dissipative Problems

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Distributed Computer and Communication Networks (DCCN 2016)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 678))

Abstract

The use of variational methods for the construction of sufficiently accurate approximate solutions of a given system requires the existence of the corresponding variational principle - a solution of the inverse problems of the calculus of variations. In the frame of the Euler’s functionals there may not exist variational principles. But if we extend the class of functionals then it could allow to get the variational formulations of the given problems. There naturally arises the problem of the constructive determination of the corresponding functionals - nonclassical Hamilton’s actions - and their application for the search of approximate solutions of the given boundary value problems. The main goal of the paper is to present a scheme for the construction of indirect variational formulations for given evolutionary problems and to demonstrate the effective use of the nonclassical Hamilton’s action for the construction of approximate solutions with the high accuracy for the given dissipative problem.

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References

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Acknowledgments

This paper was financially supported by the Ministry of Education and Science of the Russian Federation on the program to improve the competitiveness of Peoples’ Friendship University among the world’s leading research and education centers in the 2016-2020.

The work was also supported by RFBR grant No. 16-01-00450.

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Authors and Affiliations

  1. Peoples’ Friendship University of Russia, Miklukho-Maklaya str. 6, 117198, Moscow, Russia

    Vladimir Savchin & Svetlana Budochkina

Authors
  1. Vladimir Savchin
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  2. Svetlana Budochkina
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Corresponding author

Correspondence to Vladimir Savchin .

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Editors and Affiliations

  1. V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    Vladimir M. Vishnevskiy

  2. RUDN University , Moscow, Russia

    Konstantin E. Samouylov

  3. V.A. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    Dmitry V. Kozyrev

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Savchin, V., Budochkina, S. (2016). Nonclassical Hamilton’s Actions and the Numerical Performance of Variational Methods for Some Dissipative Problems. In: Vishnevskiy, V., Samouylov, K., Kozyrev, D. (eds) Distributed Computer and Communication Networks. DCCN 2016. Communications in Computer and Information Science, vol 678. Springer, Cham. https://doi.org/10.1007/978-3-319-51917-3_53

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  • DOI: https://doi.org/10.1007/978-3-319-51917-3_53

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-51916-6

  • Online ISBN: 978-3-319-51917-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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