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- Arévalo, Carmen, et al.
(författare)
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A collocation formulation of multistep methods for variable step-size extensions
- 2002
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Ingår i: Applied Numerical Mathematics. - 0168-9274. ; 42:1-3, s. 5-16
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Tidskriftsartikel (refereegranskat)abstract
- Multistep methods are classically constructed by specially designed difference operators on an equidistant time grid. To make them practically useful, they have to be implemented by varying the step-size according to some error-control algorithm. It is well known how to extend Adams and BDF formulas to a variable step-size formulation. In this paper we present a collocation approach to construct variable step-size formulas. We make use of piecewise polynomials to show that every k-step method of order k + I has a variable step-size polynomial collocation formulation. (C) 2002 IMACS. Published by Elsevier Science B.V. All rights reserved.
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| 2. |
- Arévalo, Carmen, et al.
(författare)
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Regular and singular β-blocking of difference corrected multistep methods for nonstiff index-2 DAEs
- 2000
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Ingår i: Applied Numerical Mathematics. - 0168-9274. ; 35:4, s. 293-305
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Tidskriftsartikel (refereegranskat)abstract
- There are several approaches to using nonstiff implicit linear multistep methods for solving certain classes of semi-explicit index 2 DAEs. Using β-blocked discretizations (Arevalo et al., 1996) Adams-Moulton methods up to order 4 and difference corrected BDF (Soderlind, 1989) methods up to order 7 can be stabilized. As no extra matrix computations are required, this approach is an alternative to projection methods.Here we examine some variants of β-blocking. We interpret earlier results as regular β-blocking and then develop singular β-blocking. In this nongeneric case the stabilized formula is explicit, although the discretization of the DAE as a whole is implicit. We investigate which methods can be stabilized in a broad class of implicit methods based on the BDF ρ polynomials. The class contains the BDF, Adams-Moulton and difference corrected BDF methods as well as other high order methods with small error constants. The stabilizing difference operatorτ is selected by a minimax criterion for the moduli of the zeros of σ+τ. The class of explicit methods suitable as β-blocked methods is investigated. With singular β-blocking, Adams-Moulton methods up to order 7 can be stabilized with the stabilized method corresponding to the Adams-Bashforth methods.
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| 3. |
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| 4. |
- Diaz, José, et al.
(författare)
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A wavelet semidiscretisation of elastic multibody systems
- 2003
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Ingår i: Zeitschrift für Angewandte Mathematik und Mechanik. - : Wiley. - 0044-2267. ; 83:10, s. 677-689
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Tidskriftsartikel (refereegranskat)abstract
- In this paper we consider a coupled system of elastic and rigid bodies. It can be mathematically formulated as a coupled system of ordinary and partial differential equations, often written in its weak form. The discretisation is performed by a Galerkin-type ansatz in connection with a finite element approach or known eigenfunctions. Here, we demonstrate instead the use of a recently published Galerkin-wavelet method and its application to obtain a reasonable,small number of elastic modes.
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| 5. |
- Franke, Cornelia, et al.
(författare)
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Collocation Methods for the Investigation of Periodic Motions of Constrained Multibody Systems
- 2001
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Ingår i: Multibody System Dynamics. - 1384-5640. ; 5:2, s. 133-158
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Tidskriftsartikel (refereegranskat)abstract
- The investigation of periodic motions of constrained multibody systems requires the numerical solution of differential-algebraic boundary value problems. After briefly surveying the basics of periodic motion analysis the paper presents an extension of projected collocation methods [6] to a special class of boundary Value problems for multibody system equations with position and velocity constraints. These methods can be applied for computing stable as well as unstable periodic motions. Furthermore they provide stability information, which can be used to detect bifurcations on periodic branches. The special class of equations stemming from contact problems like in railroad systems [22] can be handled as well. Numerical experiments with a wheelset model demonstrate the performance of the algorithms
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