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1994 | 29 | 1 | 267-274
Tytuł artykułu

Implicit Runge-Kutta methods for transferable differential-algebraic equations

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The numerical solution of transferable differential-algebraic equations (DAE's) by implicit Runge-Kutta methods (IRK) is studied. If the matrix of coefficients of an IRK is non-singular then the arising systems of nonlinear equations are uniquely solvable. These methods are proved to be stable if an additional contractivity condition is satisfied. For transferable DAE's with smooth solution we get convergence of order $min(k_E,k_I + 1)$, where $k_E$ is the classical order of the IRK and $k_I$ is the stage order. For transferable DAE's with generalized solution convergence of order 1 is ensured, provided that $k_E ≥ 1$.
Słowa kluczowe
Rocznik
Tom
29
Numer
1
Strony
267-274
Opis fizyczny
Daty
wydano
1994
Twórcy
autor
  • Department of Mathematics, University of Rostock, Universitätsplatz 1, D-18051 Rostock, Germany
Bibliografia
  • [Arn90] M. Arnold, Numerische Behandlung von semi-expliziten Algebrodifferentialgleichungen vom Index 1 mit linear-impliziten Verfahren, PhD thesis, Martin-Luther-Universität Halle, Sektion Mathematik, 1990.
  • [But87] J. C. Butcher, The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and General Linear Methods, Wiley, Chichester 1987.
  • [DHZ87] P. Deuflhard, E. Hairer and J. Zugck, One-step and extrapolation methods for differential-algebraic systems, Numer. Math. 51 (1987), 501-516.
  • [GM86] E. Griepentrog and R. März, Differential-Algebraic Equations and Their Numerical Treatment, Teubner-Texte Math. 88, Leipzig 1986.
  • [HLR89] E. Hairer, Ch. Lubich and M. Roche, The Numerical Solution of Differential-Algebraic Systems by Runge-Kutta Methods, Lecture Notes in Math. 1409, Springer, Berlin 1989.
  • [Ob90] H. Oberdörfer, Zur numerischen Behandlung von Algebrodifferentialgleichungen mit Runge-Kutta-Verfahren, PhD thesis, Ernst-Moritz-Arndt-Universität Greifswald, Sektion Mathematik, 1990.
  • [ORh70] J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York 1970.
  • [Pe86] L. R. Petzold, Order results for implicit Runge-Kutta methods applied to differential/algebraic systems, SIAM J. Numer. Anal. 23 (1986), 837-852.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-bcpv29z1p267bwm
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