Inmaculada Higueras, Roswitha März
Preprint series: Institut für Mathematik, Humboldt-Universität
zu Berlin (ISSN 0863-0976), 30
MSC 2000
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34A09 Implicit equations, differential-algebraic equations
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65L80 Methods for differential-algebraic equations
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65L06 Multistep, Runge-Kutta and extrapolation methods
Abstract
When
modeling complex processes by means of DAEs, one should carefully investigate
the leading term. In this paper we study properly formulated problems,
i.e. problems of the form f((Dx)',x,t)=0 with some additional condition
on im D(t). From the numerical point of view, working with properly formulated
problems in some sense means that the ODE method is used to discretize
only the differential components. We provide stability inequalities and
prove convergence in compact integration intervals for Runge-Kutta methods
and BDFs. The case of a time invariant im D(t) is essentially favourable
for the qualitative behaviour of the approximation on infinite intervals.
This study is extended to the nonlinear version f((d(x,t))', x, t)=0.
Keywords:
Differential algebraic equation, Runge-Kutta methods, backward differentiation
formulas