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Zh. Vychisl. Mat. Mat. Fiz., 2009, Volume 49, Number 9, Pages 1594–1608 (Mi zvmmf4752)  

This article is cited in 2 scientific papers (total in 2 papers)

Three-layer finite difference method for solving linear differential algebraic systems of partial differential equations

S. V. Gaidomak

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

Abstract: A boundary value problem is examined for a linear differential algebraic system of partial differential equations with a special structure of the associate matrix pencil. The use of an appropriate transformation makes it possible to split such a system into a system of ordinary differential equations, a hyperbolic system, and a linear algebraic system. A three-layer finite difference method is applied to solve the resulting problem numerically. A theorem on the stability and the convergence of this method is proved, and some numerical results are presented.

Key words: differential algebraic systems of partial differential equations, three-layer finite difference method, stability, convergence.

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English version:
Computational Mathematics and Mathematical Physics, 2009, 49:9, 1521–1534

Bibliographic databases:

UDC: 519.63
Received: 19.02.2008

Citation: S. V. Gaidomak, “Three-layer finite difference method for solving linear differential algebraic systems of partial differential equations”, Zh. Vychisl. Mat. Mat. Fiz., 49:9 (2009), 1594–1608; Comput. Math. Math. Phys., 49:9 (2009), 1521–1534

Citation in format AMSBIB
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\by S.~V.~Gaidomak
\paper Three-layer finite difference method for solving linear differential algebraic systems of partial differential equations
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2009
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\pages 1594--1608
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\pages 1521--1534
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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. S. V. Gaidomak, “On the stability of an implicit spline collocation difference scheme for linear partial differential algebraic equations”, Comput. Math. Math. Phys., 53:9 (2013), 1272–1291  mathnet  crossref  crossref  isi  elib  elib
    2. S. V. Svinina, A. K. Svinin, “On an initial-boundary value problem for a semilinear differential-algebraic system of partial differential equations of index $(1,0)$”, Russian Math. (Iz. VUZ), 63:5 (2019), 63–74  mathnet  crossref  crossref  isi
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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