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Analyzing the stability behaviour of solutions and their approximations in case of index-$2$ differential-algebraic systems

Authors: Roswitha März and Antonio R. Rodríguez-Santiesteban
Journal: Math. Comp. 71 (2002), 605-632
MSC (2000): Primary 65L20; Secondary 34D05
Published electronically: December 5, 2001
MathSciNet review: 1885617
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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-$2$ 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.

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Additional Information

Roswitha März
Affiliation: Humboldt-University Berlin, Institute of Mathematics, Unter den Linden 6, D-10099 Berlin, Germany

Antonio R. Rodríguez-Santiesteban
Affiliation: Dresearch Digital Media Systems, Otto-Schimgral-Str. 3, D-10319 Berlin, Germany

Keywords: Differential-algebraic equations, numerical stability, logarithmic norms, contractivity
Received by editor(s): August 25, 1999
Published electronically: December 5, 2001
Article copyright: © Copyright 2001 American Mathematical Society