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Zh. Vychisl. Mat. Mat. Fiz., 2015, Volume 55, Number 8, Pages 1299–1304 (Mi zvmmf10245)  

This article is cited in 12 scientific papers (total in 12 papers)

Estimates of the hyperbolization effect on the heat equation

E. E. Myshetskaya, V. F. Tishkin

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Miusskaya pl. 4, Moscow, 125047, Russia

Abstract: The difference between the solutions of the heat equation and its hyperbolized version is estimated. The estimates are obtained in the $L_2$ norm for the anisotropic heat equation and in the $C$ norm for the one-dimensional case with constant coefficients.

Key words: heat equation, hyperbolization, estimates of hyperbolization effect, difference schemes.

DOI: https://doi.org/10.7868/S004446691508013X

Full text: PDF file (238 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2015, 55:8, 1270–1275

Bibliographic databases:

UDC: 519.633
Received: 09.02.2015

Citation: E. E. Myshetskaya, V. F. Tishkin, “Estimates of the hyperbolization effect on the heat equation”, Zh. Vychisl. Mat. Mat. Fiz., 55:8 (2015), 1299–1304; Comput. Math. Math. Phys., 55:8 (2015), 1270–1275

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. A. A. Ilin, Yu. G. Rykov, “O blizosti traektorii dlya modelnykh kvazigazodinamicheskikh uravnenii. Lineinyi sluchai”, Preprinty IPM im. M. V. Keldysha, 2016, 090, 14 pp.  mathnet  crossref
    2. A. A. Ilyin, Yu. G. Rykov, “On the closeness of trajectories for model quasi-gasdynamic equations”, Dokl. Math., 94:2 (2016), 543–546  crossref  mathscinet  zmath  isi  elib  scopus
    3. M. D. Surnachev, V. F. Tishkin, B. N. Chetverushkin, “On conservation laws for hyperbolized equations”, Differ. Equ., 52:7 (2016), 817–823  crossref  mathscinet  zmath  isi  elib  scopus
    4. B. Chetverushkin, N. D'Ascenzo, A. Saveliev, V. Saveliev, “A kinetic model for magnetogasdynamics”, Math. Models Comput. Simul., 9:5 (2017), 544–553  mathnet  crossref  elib
    5. T. E. Moiseev, E. E. Myshetskaya, V. F. Tishkin, “O blizosti reshenii nevozmuschënnykh i giperbolizirovannykh uravnenii teploprovodnosti dlya razryvnykh nachalnykh dannykh”, Preprinty IPM im. M. V. Keldysha, 2017, 086, 15 pp.  mathnet  crossref
    6. S. Gasparin, J. Berger, D. Dutykh, N. Mendes, “Stable explicit schemes for simulation of nonlinear moisture transfer in porous materials”, J. Build. Perf. Simul., 11:2 (2018), 129–144  crossref  isi
    7. B. N. Chetverushkin, A. A. Zlotnik, “On a hyperbolic perturbation of a parabolic initial-boundary value problem”, Appl. Math. Lett., 83 (2018), 116–122  crossref  mathscinet  zmath  isi
    8. A. Ilyin, Yu. Rykov, S. Zelik, “Hyperbolic relaxation of the 2D Navier–Stokes equations in a bounded domain”, Physica D, 376:SI (2018), 171–179  crossref  mathscinet  isi
    9. B. N. Chetverushkin, “Giperbolicheskaya kvazigazodinamicheskaya sistema”, Matem. modelirovanie, 30:2 (2018), 81–98  mathnet  elib
    10. T. E. Moiseev, E. E. Myshetskaya, V. F. Tishkin, “On the closeness of solutions of unperturbed and hyperbolized heat equations with discontinuous initial data”, Dokl. Math., 98:1 (2018), 391–395  crossref  zmath  isi  scopus
    11. A. A. Lyupa, M. A. Trapeznikova, A. A. Chechina, N. G. Churbanova, “Sravnitelnyi analiz algoritmov yavnogo tipa dlya resheniya zadach filtratsii s ispolzovaniem giperbolizirovannykh uravnenii”, Preprinty IPM im. M. V. Keldysha, 2018, 248, 18 pp.  mathnet  crossref  elib
    12. E. V. Shilnikov, O. N. Bozorov, “Chislennoe issledovanie tochnosti i ustoichivosti metoda relaksatsii potokov”, Preprinty IPM im. M. V. Keldysha, 2019, 139, 12 pp.  mathnet  crossref
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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