Questions tagged [differential-algebraic-equations]

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The differential equation $u'\cdot v + A\cdot u = w$

Let $A\colon \mathbb R^n\to\mathbb R^{n\times n}$ be a matrix valued function, and $v, w\colon \mathbb R^n\to\mathbb R^n$ vector fields. I want to find a function/vector field $u\colon\mathbb R^n\to\...
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Confusion about Big O-Notation in convergence proof for differential algebraic equations

I understand almost all of this proof. But the part I can't find an explanation for is how they get the result for $r$ with the sums over the $\mathcal{O}(h^{\nu})$ all the way at the end of the proof....
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Properties of blocks in blockmatrix A if the matrix pair (E,A) is regular

I am working on a problem from the book "Differential-Algebraic Equations: Analysis and Numerical Solution" by Kunkel, Mehrmann. It is the Exercise 3 from Page 53 concerning matrix pairs $(E,A)$ and ...