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Stability preserving integration of index-1 DAEs. (English) Zbl 1041.65065
The paper is concerned with differential-algebraic equations (DAEs) of index 1 and their numerical integration. The main topic is the investigation of conditions under which certain qualitative properties of the DAE, in particular contractivity or dissipativity, are properly reflected by their numerical approximations without stepsize restriction, when numerical schemes with suitable stability properties are used. For this purpose, the DAE is required to have a “properly stated leading term” and to be “numerically qualified”. But also for not numerically qualified DAE’s, equivalent reformulations can help to obtain the desired properties, as is illustrated in several examples.

MSC:
65L80 Numerical methods for differential-algebraic equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
34A09 Implicit ordinary differential equations, differential-algebraic equations
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