Questions tagged [differential-algebraic-equations]

A differential-algebraic system of equations (DAEs) is a system of equations that either contains differential equations and algebraic equations, or is equivalent to such a system.

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a question on visualizing a state of DAE and a question from a continous time nonlinear dynamics

Could someone explain me what is the fundamental difference between the dynamical system of the kind $\dot x = f(x)$ and $E \dot x= f(x)$ where $E$ is a singular matrix with real entries. For the ...
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Constants of universal derivation on an $R$-algebra $A$ under localization ($d: S^{-1}A \to S^{-1}\Omega_{A/R}$)

Suppose that $A$ is an $R$-algebra, with both $R, A$ integral domains. Let $B = S^{-1}A$ be a localization of $A$. Let $$\partial_A: A \to M$$ $$\partial_B: B \to S^{-1}M$$ be an $R$-derivation on $A$ ...
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Implicit Euler integration scheme for DAEs

Consider following DAE \begin{bmatrix} a_{11} & a_{12} & a_{13} & 0\\ a_{21} & a_{22} & a_{23} & 0\\ 0 & 0 & 0 & 0 \end{bmatrix}\frac{\mathrm{d}}{\...
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(Approximate) Explicit solutions for mass matrix DAEs with nil-potent linear dynamics

I am writing a package to solve linear differential equations of the form $\frac{d\vec{x}}{dt} = A\vec{x}$ where $A$ is nil potent. The knowledge of the nil potency guarantees that the matrix ...
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The relation between $\ker(E)$ and the differential-algebraic equation $E\mathbf x'(t)=Ax(t)+f(t)$

A differential-algebraic equation is, loosely speaking, an equation of the form $$E\mathbf x'(t)=Ax(t)+f(t)$$ where $E,A\in\mathbb C^{n\times n}$, $t\in[0,\infty)$ and $f:[0,\infty)\to\mathbb C^n$, ...
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