On the Numerical Analysis and Visualisation of Implicit
Ordinary Differential Equations
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Co-author(s): Elishan Braun and Matthias Seiß |
Reference: Mathematics in Computer Science, 14 (2020) 281-293 |
Description: 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 around singularities of the
equation. The Vessiot theory automatically transforms an implicit
differential equation into a vector field distribution on a manifold and
thus reduces its analysis to standard problems in dynamical systems
theory like the integration of a vector field and the determination of
invariant manifolds. For the visualisation of low-dimensional situations
we adapt the streamlines algorithm of Jobard and Lefer to 2.5 and 3
dimensions. A concrete implementation in Matlab is discussed and some
concrete examples are presented. |
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