Journal ArticleDOI
Numerical solution of nonlinear differential equations with algebraic constraints I: Convergence results for backward differentiation formulas
Per Lötstedt,Linda R. Petzold +1 more
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In this article, the behavior of numerical ODE methods for the solution of systems of differential equations coupled with algebraic constraints is investigated, and it is shown that backward differentiation formulas converge with the expected order of accuracy for these systems.Abstract:
In this paper we investigate the behavior of numerical ODE methods for the solution of systems of differential equations coupled with algebraic constraints. Systems of this form arise frequently in the modelling of problems from physics and engineering; we study some particular examples from electrical networks, fluid dynamics and constrained mechanical systems. We show that backward differentiation formulas converge with the expected order of accuracy for these systems.read more
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Accurate solution of differential-algebraic optimization problems
TL;DR: In this paper, a nonlinear programming (NLP) formulation for differential algebraic control problems is proposed. But the problem is not solved in a straightforward way, and the quality of the solution is strongly dependent on the parameterization of the control profile.
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Some current CFD issues relevant to the incompressible Navier-Stokes equations
TL;DR: The goals of this paper are to carefully define a particular class of well-set incompressible Navier-Stokes problems in the continuum (partial differential equation/PDE) setting and to discuss some relevant and sometimes poorly understood issues related to these well-posed PDE problems, both in the continuity world and in its computer counterpart.
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Differential-algebraic equations
TL;DR: The final author version and the galley proof are versions of the publication after peer review that features the final layout of the paper including the volume, issue and page numbers.
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Review of Classical Approaches for Constraint Enforcement in Multibody Systems
André Laulusa,Olivier A. Bauchau +1 more
TL;DR: In this paper, the authors present a survey of the theoretical foundations for the enforcement of constraints in multibody dynamics problems, including index-3 differential algebraic equations in the presence of holonomic constraints.
References
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Book
Generalized inverses: theory and applications
Adi Ben-Israel,T. N. E. Greville +1 more
TL;DR: In this paper, the Moore of the Moore-Penrose Inverse is described as a generalized inverse of a linear operator between Hilbert spaces, and a spectral theory for rectangular matrices is proposed.
Book
Supersonic flow and shock waves
Richard Courant,Kurt Friedrichs +1 more
TL;DR: In this article, the authors proposed a method to compressible ecoulement for compressible compressible and supersonique and onde de choc Reference Record created on 2005-11-18, modified on 2016-08-08
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