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Zh. Vychisl. Mat. Mat. Fiz., 2013, Volume 53, Number 9, Pages 1460–1479 (Mi zvmmf9914)  

This article is cited in 5 scientific papers (total in 5 papers)

On the stability of an implicit spline collocation difference scheme for linear partial differential algebraic equations

S. V. Gaidomak

Institute of Dynamical Systems and Control Theory, Siberian Branch, Russian Academy of Sciences, ul. Lermontova. 134, Irkutsk, 664033, Russia

Abstract: A boundary value problem for linear partial differential algebraic systems of equations with multiple characteristic curves is examined. It is assumed that the pencil of matrix functions associated with this system is smoothly equivalent to a special canonic form. The spline collocation is used to construct for this problem a difference scheme of an arbitrary approximation order with respect to each independent variable. Sufficient conditions are found for this scheme to be absolutely stable.

Key words: linear partial differential algebraic equation, spline collocation difference scheme, stability of an implicit difference scheme.

DOI: https://doi.org/10.7868/S004446691309007X

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English version:
Computational Mathematics and Mathematical Physics, 2013, 53:9, 1272–1291

Bibliographic databases:

UDC: 519.63
Received: 28.02.2013

Citation: S. V. Gaidomak, “On the stability of an implicit spline collocation difference scheme for linear partial differential algebraic equations”, Zh. Vychisl. Mat. Mat. Fiz., 53:9 (2013), 1460–1479; Comput. Math. Math. Phys., 53:9 (2013), 1272–1291

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. S. V. Gaidomak, “Boundary value problem for a first-order linear parabolic system”, Comput. Math. Math. Phys., 54:4 (2014), 620–630  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. S. V. Gaidomak, “Numerical solution of linear differential-algebraic systems of partial differential equations”, Comput. Math. Math. Phys., 55:9 (2015), 1501–1514  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    3. S. V. Svinina, “Ob ustoichivosti splain-kollokatsionnoi raznostnoi skhemy dlya polulineinoi differentsialno-algebraicheskoi sistemy indeksa (1,0)”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 25 (2018), 93–108  mathnet  crossref
    4. S. V. Svinina, “Stability of a spline collocation difference scheme for a quasi-linear differential algebraic system of first-order partial differential equations”, Comput. Math. Math. Phys., 58:11 (2018), 1775–1791  mathnet  crossref  crossref  isi  elib
    5. S. V. Svinina, A. K. Svinin, “On the existence of a solution to some mixed problems for linear differential-algebraic partial differential equations”, Russian Math. (Iz. VUZ), 63:4 (2019), 64–74  mathnet  crossref  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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