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The Method of Fractional Steps for the Numerical Solution of a Multidimensional Heat Conduction Equation with Delay for the Case of Variable Coefficient of Heat Conductivity

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Differential and Difference Equations with Applications (ICDDEA 2019)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 333))

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Abstract

Multidimensional parabolic equations with delay effects in the time component for the case of variable coefficient of heat conductivity depending on spatial and temporal variables are considered. The method of fractional steps is constructed for the numerical solution of these equations. The order of approximation error for the constructed method, stability, and order of convergence are investigated. A theorem is obtained on the order of convergence of the method of fractional steps, which uses the methods from the general theory of difference schemes and the technique of the investigation of difference schemes for solving functional differential equations. Results of calculating test example with variable concentrated and distributed time delay are presented.

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Acknowledgements

This work was supported by RFBR Grant 19-01-00019 and Act 211 Government of the Russian Federation, contract 02.A03.21.0006.

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Authors and Affiliations

  1. Ural Federal University, Yekaterinburg, Russia

    Andrei Lekomtsev

Authors
  1. Andrei Lekomtsev
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Correspondence to Andrei Lekomtsev .

Editor information

Editors and Affiliations

  1. Department of Exact Sciences and Engineering, Military Academy, Lisbon, Portugal

    Sandra Pinelas

  2. Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, USA

    John R. Graef

  3. Mathematik und Didaktik, Katholische Universität Eichstätt, Eichstätt, Bayern, Germany

    Stefan Hilger

  4. Huazhong University of Science and Technology, Wuhan, Hubei, China

    Peter Kloeden

  5. Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi, Xanthi, Greece

    Christos Schinas

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Lekomtsev, A. (2020). The Method of Fractional Steps for the Numerical Solution of a Multidimensional Heat Conduction Equation with Delay for the Case of Variable Coefficient of Heat Conductivity. In: Pinelas, S., Graef, J.R., Hilger, S., Kloeden, P., Schinas, C. (eds) Differential and Difference Equations with Applications. ICDDEA 2019. Springer Proceedings in Mathematics & Statistics, vol 333. Springer, Cham. https://doi.org/10.1007/978-3-030-56323-3_9

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