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Differential — Algebraic Equations
2003Differential — 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
2012In 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 +2 more
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Differential-Algebraic Equations: A Tutorial Review
International Journal of Bifurcation and Chaos, 1998This article (Funded by EPSRC and the National Grid Company.) explores some introductory principles of differential-algebraic equations (DAEs) and makes a connection with the theory of dynamical systems. Some results which are new in the field of DAEs are also surveyed.
Beardmore, R. E., Song, Y. H.
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Solvability of General Differential Algebraic Equations
SIAM Journal on Scientific Computing, 1995Summary: In the last few years there has been considerable research on differential algebraic equations (DAE) \(f(t,x,x') = 0\) where \(f_{x'}\) is identically singular. Most of this effort has focused on computing a solution that is assumed to exist. That is, the DAE is assumed solvable.
Campbell, Stephen L., Griepentrog, E.
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Solutions of Linear Differential Algebraic Equations
SIAM Review, 1998Summary: The authors show how to solve inhomogeneous linear differential algebraic systems with constant coefficients.
Shirvani, Mazi, So, Joseph W.-H.
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Structural analysis of integro-differential–algebraic equations
Journal of Computational and Applied Mathematics, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Reza Zolfaghari +2 more
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Differential-Algebraic Equation Index Transformations
SIAM Journal on Scientific and Statistical Computing, 1988The 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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Index-2 Differential-Algebraic Equations
Results in Mathematics, 1989A class of general nontransferable differential-algebraic equations which contains all linear differential-algebraic equations having the global index 2 in the definition of Gear and Petzold or being tractable with index 2 in the sense of Griepentrog and März as well as nonlinear index-2 equations in the understanding of Brenan, Gear, Petzold and ...
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Regularization of Nonlinear Differential-Algebraic Equations
SIAM Journal on Mathematical Analysis, 1994Summary: This paper illustrates how initial value problems for nonlinear differential-algebraic equations can be regularized, i.e., converted to tractable singularly perturbed problems, by appropriate introduction of a small positive parameter \(\varepsilon\).
O'Malley, Robert E. jun. +1 more
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Abstract differential-algebraic equations
2013The concept of regular DAEs developed in Part I for DAEs in finite-dimensional spaces is generalized to some extend for DAEs acting in Hilbert spaces, which are called abstract differential-algebraic equations (ADAEs). Such a framework aims to provide a systematic approach for coupled systems of different type. It should be emphasized that this working
René Lamour +2 more
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