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Index Concepts for Differential-Algebraic Equations

, 2015
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Numerical integration of stiff differential/algebraic equations of flexible multibody systems.

Bassam A. Hussein
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Differential Equations in Banach Algebras

Doklady Mathematics, 2020
In a complex Banach algebra \(\mathbb{B}\) the ordinary linear differential equation \[ \mathbf{x}^{(n)} + \mathbf{p}_1\mathbf{x}^{(n-1)} + \dots + \mathbf{p}_{n-1}\dot{\mathbf{x}} + \mathbf{p}_ n \mathbf{x} = 0 \tag{1} \] with constant coefficients is considered.
Perov, A. I., Kostrub, I. D.
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Differential-Algebraic Equations

Oberwolfach Reports, 2007
The topic of Differential Algebraic Equations (DAEs) began to attract significant research interest in applied and numerical mathematics in the early 1980's. Today, a quarter of a century later, DAEs are an independent field of research, which is gaining in importance and becoming of increasing interest for both applications and mathematical theory.
Stephen L. Campbell, Roswitha März, Linda Petzold, Peter Rentrop   +3 more
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Differential — Algebraic Equations

2003
Differential — algebraic equations (DAE) differ from other problems with solutions given by smooth and continuous parametric sets. They combine specifics of the nonlinear algebraic or transcendental equations with those of ODE. Correct formulation of the Cauchy problem for such equations requires solution of a system of nonlinear equations.
V. I. Shalashilin, E. B. Kuznetsov
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Differential Algebraic Equations

2017
This chapter documents how to formulate and solve optimization problems with differential and algebraic equations (DAEs). The pyomo.dae package allows users to easily incorporate detailed dynamic models within an optimization framework and is flexible enough to represent a wide variety of differential equations.
William E. Hart, Carl D. Laird, Jean-Paul Watson, David L. Woodruff, Gabriel A. Hackebeil, Bethany L. Nicholson, John D. Siirola   +6 more
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Differential Algebraic Equations

2012
In Chaps. 2 and 3 we were concerned mainly with the numerical solution of ordinary differential equations of the form y′ = f(x, y). However, there are problems which are more general than this and require special methods for their solution. One such class of problems are differential algebraic equations (DAEs).
Karline Soetaert, Jeff Cash, Francesca Mazzia   +2 more
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Differential-Algebraic Equations

2016
In this chapter, we introduce the differential algebraic equations which we abbreviate as DAEs. DAEs arise in a variety of applications such as modelling constrained multibody systems, electrical networks, aerospace engineering, chemical processes, computational fluid dynamics, gas transport networks, see [10–12, 35].
N. Banagaaya, G. Alì, W. H. A. Schilders   +2 more
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Differential-Algebraic Equation Index Transformations

SIAM Journal on Scientific and Statistical Computing, 1988
The index of an implicit system of differential equations, also known as a differential algebraic equation or DAE, measures how far, in some sense, the system is from being an explicit ordinary differential equation. There is interest in many areas of applications in working directly with the implicit models that often arise.
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