A Half-Explicit Extrapolation Method for Differential-Algebraic Systems of Indix 3

Ostermann, Alexander

doi:10.1093/imanum/10.2.171

Cited by 7 publications

(1 citation statement)

References 8 publications

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“…Unfortunately, this class of so called "index-Y' DAEs, is not solvable by state-of-the-art numerical software, although some theoretical work on variable step-size discretization schemes has recently appeared [14,21].…”

Section: = G(p)b + G"(p)(vv) =: G(p)b + Z(p V)mentioning

confidence: 99%

Numerical solution of differential-algebraic equations for constrained mechanical motion

Führer¹,

Leimkuhler

1991

Numer. Math.

139

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Summary.The two most popular formulations of the equations of constrained mechanical motion, the descriptor and state-space forms, each have severe practical limitations. In this paper, we discuss and relate some proposed reformulations of the equations which have improved numerical properties. Subject classifications. AMS(MOS): 65L05; CR: G1.7 I IntroductionWe are concerned with the equations of constrained mechanical motion. The equations are typically developed from variational principles, and the resulting system, which can be considered a differential equation on a manifold, is mapped to an ordinary differential equation [2]. The mapping is not easily automated, nor necessarily desirable in the computational setting, while the original constrained statement of the problem is not solvable by current numerical software.Two alternative formulations have recently been discussed in the literature, one based on an overdetermined system of equations including time derivatives of the constraints, and the other based on stabilization with respect to those differentiated constraints via additional Lagrange multipliers. These formulations lead to systems of equations which are more amenable to numerical computation than either of the two traditional models. In the sequel we discuss and relate the reformulations, in the context of numerical discretization.Historically, mechanical systems have been formulated as Lagrange equations of the first or second kind. The Lagrangian equations of the first kind, derived directly from variational principles, are a constrained differential equation or a differential-algebraic equation (DAE): Offprint requests to: C. Fiihrer

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Section: = G(p)b + G"(p)(vv) =: G(p)b + Z(p V)mentioning

confidence: 99%

Numerical solution of differential-algebraic equations for constrained mechanical motion

Führer¹,

Leimkuhler

1991

Numer. Math.

139

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Numerical Methods for Differential‐Algebraic Equations with Application to Real‐Times Simulation of Mechanical Systems

Potra

1994

Z Angew Math Mech

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A class of half-explicit Runge-Kutta methods for differential-algebraic systems of index 3

Ostermann

1993

Applied Numerical Mathematics

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A Half-Explicit Extrapolation Method for Differential-Algebraic Systems of Indix 3

Cited by 7 publications

References 8 publications

Numerical solution of differential-algebraic equations for constrained mechanical motion

Numerical solution of differential-algebraic equations for constrained mechanical motion

Numerical Methods for Differential‐Algebraic Equations with Application to Real‐Times Simulation of Mechanical Systems

A class of half-explicit Runge-Kutta methods for differential-algebraic systems of index 3

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