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Zh. Vychisl. Mat. Mat. Fiz., 2017, Volume 57, Number 5, Pages 801–813 (Mi zvmmf10571)  

This article is cited in 6 scientific papers (total in 6 papers)

The projection Galerkin method for solving the time-independent differential diffusion equation in a semi-infinite domain

A. M. Makarenkova, E. V. Sereginaa, M. A. Stepovichb

a Kaluga Division of the Moscow State Technical University, Kaluga, Russia
b Kaluga State University, Kaluga, Russia

Abstract: Using the diffusion equation as an example, results of applying the projection Galerkin method for solving time-independent heat and mass transfer equations in a semi-infinite domain are presented. The convergence of the residual corresponding to the approximate solution of the timeindependent diffusion equation obtained by the projection method using the modified Laguerre functions is proved. Computational results for a two-dimensional toy problem are presented.

Key words: heat and mass transfer equations, diffusion, projection Galerkin method, Laguerre functions.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 340/2015, 1416
Russian Foundation for Basic Research 16-03-00515_
14-42-03062___


DOI: https://doi.org/10.7868/S0044466917050076

Full text: PDF file (206 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2017, 57:5, 802–814

Bibliographic databases:

UDC: 519.62
Received: 28.03.2016

Citation: A. M. Makarenkov, E. V. Seregina, M. A. Stepovich, “The projection Galerkin method for solving the time-independent differential diffusion equation in a semi-infinite domain”, Zh. Vychisl. Mat. Mat. Fiz., 57:5 (2017), 801–813; Comput. Math. Math. Phys., 57:5 (2017), 802–814

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. A. Abilov, F. V. Abilova, M. K. Kerimov, “On sharp estimates of the convergence of double Fourier–Bessel series”, Comput. Math. Math. Phys., 57:11 (2017), 1735–1740  mathnet  crossref  crossref  isi  elib
    2. V E. Seregina, A. N. Polyakov, M. A. Stepovich, “On the possibility of using the Galerkin projection method to simulate the two-dimensional diffusion of excitons generated by an electron beam”, Computer Simulations in Physics and Beyond (CSP2017), Journal of Physics Conference Series, 955, IOP Publishing Ltd, 2018, 012032  crossref  isi  scopus
    3. Seregina E.V. Stepovich M.A. Kalmanovich V.V., International Conference on Computer Simulation in Physics and Beyond, Journal of Physics Conference Series, 1163, ed. Shchur L., IOP Publishing Ltd, 2019  crossref  isi
    4. E. V. Seregina, V. V. Kalmanovich, M. A. Stepovich, “Sravnitelnyi analiz matrichnogo metoda i metoda konechnykh raznostei dlya modelirovaniya raspredeleniya neosnovnykh nositelei zaryada v mnogosloinoi planarnoi poluprovodnikovoi strukture”, Materialy Voronezhskoi zimnei matematicheskoi shkoly Sovremennye metody teorii funktsii i smezhnye problemy. 28 yanvarya2 fevralya 2019 g. Chast 3, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 172, VINITI RAN, M., 2019, 104–112  mathnet  crossref
    5. E. V. Seregina, M. A. Stepovich, V. V. Kalmanovich, “O nakhozhdenii momentnykh funktsii stokhasticheskogo protsessa teploprovodnosti s ispolzovaniem proektsionnogo metoda”, Materialy Voronezhskoi vesennei matematicheskoi shkoly Sovremennye metody teorii kraevykh zadach. Pontryaginskie chteniyaXXX. Voronezh, 39 maya 2019 g. Chast 3, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 192, VINITI RAN, M., 2021, 102–110  mathnet  crossref
    6. E. V. Seregina, M. A. Stepovich, A. M. Makarenkov, “O nakhozhdenii momentnykh funktsii resheniya stokhasticheskogo uravneniya diffuzii s ispolzovaniem proektsionnogo metoda”, Materialy 20 Mezhdunarodnoi Saratovskoi zimnei shkoly «Sovremennye problemy teorii funktsii i ikh prilozheniya», Saratov, 28 yanvarya — 1 fevralya 2020 g. Chast 2, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 200, VINITI, M., 2021, 105–114  mathnet  crossref
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