Journal of engineering physics

, Volume 42, Issue 6, pp 687–692 | Cite as

Method of reduction to the ordinary differential equations of L. V. Kantorovich and a general method for the solution of multidimensional heat-transfer equations

  • V. G. Prokopov
  • E. I. Bespalova
  • Yu. V. Sherenkovskii


A method is proposed for the solution of multidimensional heat-transfer problems, representing a further elaboration and generalization of projection methods.


Differential Equation Statistical Physic Ordinary Differential Equation Projection Method 
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Literature cited

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    S. G. Mikhlin, Numerical Implementation of Variational Methods [in Russian], Nauka, Moscow (1966).Google Scholar
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    M. A. Krasnosel'skii, G. M. Bainikko, P. P. Zabreiko, et al., Approximate Solution of Operator Equations [in Russian], Nauka, Moscow (1969).Google Scholar
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    L. V. Kantorovich, “A direct method for the approximate solution of the problem of the minimum of a double integral,” Izv. Akad. Nauk SSSR, Otd. Mat. Estestv. Nauk, No. 5, 647–653 (1933).Google Scholar
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    M. F. Kravchuk, Reduction of the Method of Moments to the Solution of Linear Differential and Integral Equations [in Ukrainian], Vid. Ukr. Akad. Nauk, Kiev (1936).Google Scholar
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    L. Collatz, The Numerical Treatment of Differential Equations (3rd ed.), Springer-Verlag, Berlin (1966).Google Scholar
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    V. G. Prokopov, E. I. Bespalova, and Yu. V. Sherenkovskii, “A new method for the mathematical investigation of transport processes,” Prom-st. Teplotekh., No. 2, 33–41 (1979).Google Scholar

Copyright information

© Plenum Publishing Corporation 1982

Authors and Affiliations

  • V. G. Prokopov
    • 1
  • E. I. Bespalova
    • 1
  • Yu. V. Sherenkovskii
    • 1
  1. 1.Kiev Polytechnic InstituteUSSR

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