Matthias Seiß

activity

20142025

most citedOn the Numerical Analysis and Visualisation of Implicit Ordinary Differential Equations

7 citations · 13 across the 13 of their papers we have counts for

collaborators

15 papers

math.RT2025

On the Direct Problem in Differential Galois Theory for the Classical Groups

Daniel Robertz, Matthias Seiss

Let $G$ be a classical group of Lie rank $l$ and let $C$ be an algebraically closed field of characteristic zero. For $l$ differential indeterminates $\boldsymbol{v}=(v_1,\dots,v_l…

math.AC2025

Iterated and Generalized Iterated Integrals

Chitrarekha Sahu, Matthias Seiss, Varadharaj Ravi Srinivasan

For a differential field $F$ having an algebraically closed field of constants, we analyze the structure of Picard-Vessiot extensions of $F$ whose differential Galois groups are un…

math.DS2023★ 1 cited

Identifying Markov chain models from time-to-event data: an algebraic approach

Ovidiu Radulescu, Dima Grigoriev, Matthias Seiss +3

Many biological and medical questions can be modeled using time-to-event data in finite-state Markov chains, with the phase-type distribution describing intervals between events. W…

math.NA2023

On the Numerical Integration of Singular Initial and Boundary Value Problems for Generalised Lane-Emden and Thomas-Fermi Equations

Werner M. Seiler, Matthias Seiss

We propose a geometric approach for the numerical integration of singular initial value problems for (systems of) quasi-linear differential equations. It transforms the original pr…

math.DS2022

A Computational Approach to Polynomial Conservation Laws

Aurélien Desoeuvres, Alexandru Iosif, Christoph Lüders +4

For polynomial ODE models, we introduce and discuss the concepts of exact and approximate conservation laws, which are the first integrals of the full and truncated sets of ODEs. F…

math.DS2022

Reduction of Chemical Reaction Networks with Approximate Conservation Laws

Aurélien Desoeuvres, Alexandru Iosif, Christoph Lüders +4

Model reduction of fast-slow chemical reaction networks based on the quasi-steady state approximation fails when the fast subsystem has first integrals. We call these first integra…

math.AC2022

Normal Forms in Differential Galois Theory for the Classical Groups

Daniel Robertz, Matthias Seiss

Let $G$ be a classical group of dimension $d$ and let $a = (a_{1}, \dots, a_{d})$ be differential indeterminates over a differential field $F$ of characteristic zero with alge…

math.AC2020

On General Extension Fields for the Classical Groups in Differential Galois Theory

Matthias Seiss

Let $G$ be one of the classical groups of Lie rank $l$ . We make a similar construction of a general extension field in differential Galois theory for $G$ as E. Noether did in class…

math.DS2020★ 7 cited

On the Numerical Analysis and Visualisation of Implicit Ordinary Differential Equations

Elishan Braun, Werner M. Seiler, Matthias Seiss

We discuss how the geometric theory of differential equations can be used for the numerical integration and visualisation of implicit ordinary differential equations, in particular…

math.LO2020★ 3 cited

A Logic Based Approach to Finding Real Singularities of Implicit Ordinary Differential Equations

Werner M. Seiler, Matthias Seiss, Thomas Sturm

We discuss the effective computation of geometric singularities of implicit ordinary differential equations over the real numbers using methods from logic. Via the Vessiot theory o…

math.AC2020

Singularities of Algebraic Differential Equations

Markus Lange-Hegermann, Daniel Robertz, Werner M. Seiler +1

There exists a well established differential topological theory of singularities of ordinary differential equations. It has mainly studied scalar equations of low order. We propose…

math.DS2020

No Chaos in Dixon's System

Werner M. Seiler, Matthias Seiss

The so-called Dixon system is often cited as an example of a two-dimensional (continuous) dynamical system that exhibits chaotic behaviour, if its two parameters take their value i…

math.DS2020

Singular Initial Value Problems for Scalar Quasi-Linear Ordinary Differential Equations

Werner M. Seiler, Matthias Seiss

We discuss existence, non-uniqueness and regularity of one- and two-sided solutions of initial value problems for scalar quasi-linear ordinary differential equations where the init…

math.RA2016★ 1 cited

Root Parametrized Differential Equations for the classical groups

Matthias Seiß

Let $C ⟨ t_{1}, \dots t_{l} ⟩$ be the differential field generated by $l$ differential indeterminates $t = (t_{1}, \dots, t_{l})$ over an algebraically closed field $…

math.AC2014★ 1 cited

A Root Parametrized Differential Equation for the Special Linear Group

Matthias Seiß

Let $C ⟨ t ⟩$ be the differential field generated by $l$ differential indeterminates $t = (t_{1}, \dots, t_{l})$ over an algebraically closed field…