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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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The Transfer Matrix of Differential-Algebraic Equations
Siberian Mathematical Journal, 2022This paper is devoted to the study of the transfer function of linear differential-algebraic equations. The author considers the system \[ \begin{aligned} A\frac{d}{dt} x(t) + Bx(t)+ Uu(t)=&0,\quad t\in T=[0,\infty) \\ y(t)=Cx&(t), \end{aligned}\tag{1} \] with some known real \(n \times n\) matrices \(A\) and \(B\), such that \(\mathrm{det} A = 0\), an
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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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On the robust stability of Volterra differential–algebraic equations
Systems & Control Letters, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Regularizations of Differential‐Algebraic Equations Revisited
Mathematische Nachrichten, 1995AbstractThe present paper deals with quasilinear differential‐algebraic equations with index 2. These equations are approximated by regularization methods. Such methods lead to singularly perturbed differential‐algebraic equations. Using a geometric theory of singular perturbations convergence of the solutions of the regularized problems towards that ...
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On the Superstability of an Interval Family of Differential-Algebraic Equations
Automation and Remote Control, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Differential-Algebraic Equations
1984In this paper we study the numerical solution of the differential/algebraic systems F(t, y, y′) = 0. Many of these systems can be solved conveniently and economically using a range of ODE methods. Others can be solved only by a small subset of ODE methods, and still others present insurmountable difficulty for all current ODE methods.
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On the Optimum Control of Differential-Algebraic Equations
Journal of Optimization Theory and Applications, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Multistep methods for differential algebraic equations
Numerical Algorithms, 1995Multistep methods for specially structured implicit nonlinear differential algebraic equations under index 1 conditions are considered. The existence and uniqueness of a numerical solution is shown. There is no discussion about the progress of this paper in comparison to previous ones, e.g. \textit{E. Griepentrog} and \textit{R.
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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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