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Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 9, Pages 1643–1651 (Mi zvmmf4756)  

This article is cited in 10 scientific papers (total in 10 papers)

Error estimates for the Galerkin method as applied to time-dependent equations

P. V. Vinogradova, A. G. Zarubin

Far Eastern State Transport University, ul. Serysheva 47, Khabarovsk, 680021, Russia

Abstract: A projection method is studied as applied to the Cauchy problem for an operator-differential equation with a non-self-adjoint operator. The operator is assumed to be sufficiently smooth. The linear spans of eigenelements of a self-adjoint operator are used as projection subspaces. New asymptotic estimates for the convergence rate of approximate solutions and their derivatives are obtained. The method is applied to initial-boundary value problems for parabolic equations.

Key words: Galerkin method, operator equation, Hilbert space, Cauchy problem, convergence rate, orthoprojector, parabolic equations.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:9, 1567–1575

Bibliographic databases:

UDC: 519.63
Received: 06.10.2008
Revised: 12.01.2009

Citation: P. V. Vinogradova, A. G. Zarubin, “Error estimates for the Galerkin method as applied to time-dependent equations”, Zh. Vychisl. Mat. Mat. Fiz., 49:9 (2009), 1643–1651; Comput. Math. Math. Phys., 49:9 (2009), 1567–1575

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Egorov I.E., Tikhonova I.M., “O skorosti skhodimosti statsionarnogo metoda galerkina dlya uravneniya smeshannogo tipa”, Vestn. Yuzhno-Uralskogo gosyu un-ta. Ser. Matematicheskoe modelirovanie i programmirovanie, 2012, no. 40, 53–58  zmath  elib
    2. Egorov I.E., Efimova E.S., “Otsenka pogreshnosti statsionarnogo metoda Galërkina dlya vyrozhdayuschegosya parabolicheskogo uravneniya”, Matematicheskie zametki YaGU, 19:1 (2012), 27–33  zmath  elib
    3. I. E. Egorov, I. M. Tikhonova, “O skorosti skhodimosti statsionarnogo metoda Galerkina dlya uravneniya smeshannogo tipa”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 2012, no. 14, 53–58  mathnet
    4. P. V. Vinogradova, T. E. Koroleva, “One projection method for linear equation of third order”, Russian Math. (Iz. VUZ), 58:11 (2014), 22–27  mathnet  crossref
    5. I. E. Egorov, I. M. Tikhonova, “Modifitsirovannyi metod Galerkina dlya zadachi Vragova”, Sib. elektron. matem. izv., 12 (2015), 732–742  mathnet  crossref
    6. P. V. Vinogradova, A. M. Samusenko, I. S. Manzhula, “Asymptotic estimate of a Petrov–Galerkin method for nonlinear operator-differential equation”, Vestn. YuUrGU. Ser. Matem. modelirovanie i programmirovanie, 9:4 (2016), 17–29  mathnet  crossref  elib
    7. I. M. Tikhonova, “Primenenie statsionarnogo metoda Galerkina k pervoi kraevoi zadache dlya uravneniya smeshannogo tipa vysokogo poryadka”, Matematicheskie zametki SVFU, 23:4 (2016), 73–81  mathnet  elib
    8. V. E. Fedorov, I. M. Tikhonova, “O statsionarnom metode Galerkina v odnoi kraevoi zadache dlya uravneniya smeshannogo tipa vtorogo poryadka”, Matematicheskie zametki SVFU, 23:4 (2016), 82–90  mathnet  elib
    9. E. S. Efimova, “Statsionarnyi metod Galerkina dlya polulineinogo neklassicheskogo uravneniya vysokogo poryadka s menyayuschimsya napravleniem vremeni”, Matematicheskie zametki SVFU, 24:1 (2017), 16–25  mathnet  elib
    10. I. E. Egorov, E. S. Efimova, “Kraevaya zadacha dlya uravneniya tretego poryadka, ne razreshennogo otnositelno starshei proizvodnoi”, Matematicheskie zametki SVFU, 24:4 (2017), 28–36  mathnet  crossref  elib
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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