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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2005, Volume 45, Number 10, Pages 1848–1859 (Mi zvmmf585)  

This article is cited in 7 scientific papers (total in 7 papers)

Projection difference scheme for a parabolic functional differential equation with two-dimensional transformation of arguments

A. V. Razgulin

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia
References:
Abstract: A nonlinear parabolic functional differential equation with the functional part containing a generalized superposition of the unknown solution and a transformation of the two-dimensional spatial argument is considered. A projection difference scheme for the approximation of the initial Dirichlet boundary value problem in a rectangle is proposed for a wide class of measurable, including noninvertible, transformations. An estimate of the rate of convergence to the generalized solutions of the initial problem of order O(τ1/4γ+h1/22γ) in the norm L2(Q) without a priori assumptions on the invertibility of the transformation and without any mesh size matching is obtained.
Received: 24.05.2005
Bibliographic databases:
Document Type: Article
UDC: 519.642.2
Language: Russian
Citation: A. V. Razgulin, “Projection difference scheme for a parabolic functional differential equation with two-dimensional transformation of arguments”, Zh. Vychisl. Mat. Mat. Fiz., 45:10 (2005), 1848–1859; Comput. Math. Math. Phys., 45:10 (2005), 1780–1791
Citation in format AMSBIB
\Bibitem{Raz05}
\by A.~V.~Razgulin
\paper Projection difference scheme for a parabolic functional differential equation with two-dimensional transformation of arguments
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2005
\vol 45
\issue 10
\pages 1848--1859
\mathnet{http://mi.mathnet.ru/zvmmf585}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2189392}
\zmath{https://zbmath.org/?q=an:1097.65094}
\transl
\jour Comput. Math. Math. Phys.
\yr 2005
\vol 45
\issue 10
\pages 1780--1791
Linking options:
  • https://www.mathnet.ru/eng/zvmmf585
  • https://www.mathnet.ru/eng/zvmmf/v45/i10/p1848
  • This publication is cited in the following 7 articles:
    1. A. V. Razgulin, S. V. Sazonova, “On the matrix Fourier filtering problem for a class of models of nonlinear optical systems with a feedback”, Comput. Math. Math. Phys., 57:9 (2017), 1385–1403  mathnet  crossref  crossref  isi  elib  elib
    2. T. E. Romanenko, A. V. Razgulin, “On modeling of distortions suppression in nonlinear optical system with delayed feedback loop”, Math. Models Comput. Simul., 7:3 (2015), 259–270  mathnet  crossref  mathscinet
    3. A. V. Razgulin, T. E. Romanenko, “Rotating waves in parabolic functional differential equations with rotation of spatial argument and time delay”, Comput. Math. Math. Phys., 53:11 (2013), 1626–1643  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    4. A. M. Selitskii, “Modelirovanie nekotorykh opticheskikh sistem na osnove parabolicheskogo differentsialno-raznostnogo uravneniya”, Matem. modelirovanie, 24:12 (2012), 38–42  mathnet  mathscinet
    5. V. A. Grebennikov, A. V. Razgulin, “Weighted estimate for the convergence rate of a projection difference scheme for a quasilinear parabolic equation”, Comput. Math. Math. Phys., 51:7 (2011), 1208–1221  mathnet  crossref  mathscinet  isi  elib
    6. A. V. Razgulin, “A weighted estimate for the rate of convergence of a projection-difference scheme for a parabolic equation and its application to the approximation of the initial-data control problem”, Comput. Math. Math. Phys., 50:6 (2010), 969–983  mathnet  crossref  mathscinet  adsnasa  isi  elib  elib
    7. Razgulin A.V., “The problem of control of a two-dimensional transformation of spatial arguments in a parabolic functional-differential equation”, Differential Equations, 42:8 (2006), 1140–1155  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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