Analyzing the stability behaviour of solutions and their approximations in case of index-\(2\) differential-algebraic systems (Q2781212)
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scientific article; zbMATH DE number 1720963
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Analyzing the stability behaviour of solutions and their approximations in case of index-\(2\) differential-algebraic systems |
scientific article; zbMATH DE number 1720963 |
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19 March 2002
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differential-algebraic equations
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numerical stability
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logarithmic norms
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contractivity
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index 2
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numerical examples
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tractability index
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Runge-Kutta methods
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Hessenberg systems
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Analyzing the stability behaviour of solutions and their approximations in case of index-\(2\) differential-algebraic systems (English)
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The stability behaviour of the solutions and their approximations of linear index 2 differential-algebraic systems is analyzed. Using the tractability index concept (whose fundamentals are introduced) the differential-algebraic equation (DAE) and discretizations (BDE and Runge-Kutta methods) are decoupled and the effect of the integration method on the inherent ordinary differential equation (ODE) is investigated. Sufficient conditions are given to guarantee that the integration method applied to the original DAE generates the same solutions as the direct application to the inherent ODE could do. Hessenberg systems are used throughout the paper to illustrate the various steps. Two examples (a ``good'' and a ``bad'' one) prove the results.
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