| 1. |
- Arévalo, Carmen, et al.
(författare)
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Stabilized multistep methods for index 2 Euler-Lagrange DAEs
- 1996
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Ingår i: BIT. - 0006-3835. ; 36:1, s. 1-13
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Tidskriftsartikel (refereegranskat)abstract
- We consider multistep discretizations, stabilized by β-blocking, for Euler-Lagrange DAEs of index 2. Thus we may use “nonstiff” multistep methods with an appropriate stabilizing difference correction applied to the Lagrangian multiplier term. We show that order p =k + 1 can be achieved for the differential variables with order p =k for the Lagrangian multiplier fork-step difference corrected BDF methods as well as for low order k-step Adams-Moulton methods. This approach is related to the recently proposed “half-explicit” Runge-Kutta methods.
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| 2. |
- Arévalo, Carmen, et al.
(författare)
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β-blocked multistep methods for Euler-Lagrange DAEs: Linear analysis
- 1997
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Ingår i: ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik. - : Wiley. - 0044-2267. ; 77:8, s. 609-617
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Tidskriftsartikel (refereegranskat)abstract
- Many different methods have been suggested for the numerical solution of index 2 and 3 Euler-Lagrange equations. We focus on 0-stability of multistep methods (φ, σ) and investigate the relations between some well-known computational techniques. By various modifications, referred to as β-blocking of the σ polynomial, some basic shortcomings of multistep methods may be overcome. This approach is related to projection techniques and has a clear and well-known analogy in control theory. In particular, it is not necessary to use BDF methods for the solution of high index problems; indeed, “nonstiff” methods may be used for part of the system provided that the state-space form is nonstiff. We illustrate the techniques and demonstrate the results with a simplified multibody model of a truck.
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| 3. |
- Eich, Edda, et al.
(författare)
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On the error control for multistep methods applied to ODEs with invariants and DAEs in multibody dynamics
- 1995
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Ingår i: Mechanics of Structures and Machines. - : Informa UK Limited. - 0890-5452. ; 23:2, s. 159-180
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Tidskriftsartikel (refereegranskat)abstract
- A modified local error model is developed for numerical integration of ODEs with invariants. The basic idea is to use a commutativity relationship that holds for implicit state-space form methods. A new implicit state-space form predictor is developed from which error estimates can be obtained by predictor-corrector difference: This technique is demonstrated through the preliminary examples in this paper.
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| 4. |
- Eich-Soellner, Edda, et al.
(författare)
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Numerische Methoden in der Mehrkörperdynamik
- 1995
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Ingår i: Mathematik in der Praxis: Fallstudien aus Industrie, Wirtschaft, Naturwissenschaften und Medizin. - 9783540592945 ; , s. 41-41
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Bokkapitel (populärvet., debatt m.m.)
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