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Analyzing the stability behaviour of solutions and their approximations in case of index- differential-algebraic systems
Author(s):
Roswitha
März;
Antonio
R.
Rodríguez-Santiesteban.
Journal:
Math. Comp.
71
(2002),
605-632.
MSC (2000):
Primary 65L20;
Secondary 34D05
Posted:
December 5, 2001
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Abstract:
When integrating regular ordinary differential equations numerically, one tries to match carefully the dynamics of the numerical algorithm with the dynamical behaviour of the true solution. The present paper deals with linear index- differential-algebraic systems. It is shown how knowledge pertaining to (numerical) regular ordinary differential equations applies provided a certain subspace which is closely related to the tangent space of the constraint manifold remains invariant.
References:
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- 2.
- R. M¨ARZ: Numerical methods for differential-algebraic equations. Acta Numerica 1992, 141-198. MR 93e:65096
- 3.
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Additional Information:
Roswitha
März
Affiliation:
Humboldt-University Berlin, Institute of Mathematics, Unter den Linden 6, D-10099 Berlin, Germany
Email:
maerz@mathematik.hu-berlin.de
Antonio
R.
Rodríguez-Santiesteban
Affiliation:
Dresearch Digital Media Systems, Otto-Schimgral-Str. 3, D-10319 Berlin, Germany
Email:
rodriguez@dresearch.de
DOI:
10.1090/S0025-5718-01-01408-9
PII:
S 0025-5718(01)01408-9
Keywords:
Differential-algebraic equations,
numerical stability,
logarithmic norms,
contractivity
Received by editor(s):
August 25, 1999
Posted:
December 5, 2001
Copyright of article:
Copyright
2001,
American Mathematical Society
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