39 citations · 118 across the 19 of their papers we have counts for
22 papers
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…
Open Covers and Lex Points of Hilbert schemes over quotient rings via relative marked bases
Cristina Bertone, Francesca Cioffi, Matthias Orth +1
We introduce the notion of a relative marked basis over quasi-stable ideals, together with constructive methods and a functorial interpretation, developing computational methods fo…
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…
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…
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…
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…