Software development for implicit singular BVPs
Objectives:
Our aim is to provide an updated version BVPSUITE 2.0 of the MATLAB
code BVPSUITE1.1 (based on collocation) for the numerical solution
of boundary value problems for systems of ODEs in implicit form.
These systems can exhibit singularity of the first or second kind.
We are also interested to solve systems of DAEs with critical points
and singular eigenvalue problems.
We give full theoretical justification of the code components,
collocation solver, error estimation procedure and grid adaptation
strategy. BVPSUITE2.0 is also equipped with a new module for
following a path in the parameter-solution space with possible
turning points. The path is followed using the pseudo-arclength
continuation with automatic step-length control.
Members of the Research Group "Numerics and Simulation of Differential Equations" involved in the project:
Winfried Auzinger |
Merlin Fallahpour |
Georg Kitzhofer |
Othmar Koch |
Gernot Pulverer |
Ewa Weinmüller |
Stefan Wurm |
Software:
You can download from here the Matlab package BVPSUITE2.0
together with manual and examples. This version BVPSUITE2.0 (Release
January 2020) can be used under the conditions of the licence
enclosed in the zip-file containing the code. If you have
suggestions or remarks concerning BVPSUITE2.0, please contact us
at e.weinmueller@tuwien.ac.at
Important publications:
O. Koch,
Asymptotically Correct Error Estimation for Collocation Methods
Applied to Singular Boundary Value Problems, Numer. Math.
101(2005), pp. 143-164.
W. Auzinger, E. Karner, O. Koch, E. B. Weinmüller, Collocation
Methods for the Solution of Eigenvalue Problems for Singular
Ordinary Differential Equations, Opuscula Math. 26/2(2006),
pp. 229-241.
G. Kitzhofer, O. Koch, E. B. Weinmüller,
Pathfollowing
for Essentially Singular Boundary Value Problems with Application
to the Complex Ginzburg-Landau Equation, BIT Numer. Math.
49(2009), pp. 217-245.
G. Pulverer, G. Söderlind, E. Weinmüller, Automatic
Grid Control in Adaptive BVP Solvers, Numer. Algorithms
56(2011), pp. 61-92.
W.
Auzinger, O. Koch, E.B. Weinmüller, S. Wurm, Modular
version bvpsuite1.2 of the collocation MATLAB package
bvpsuite1.1, Technical Report ASC 30/2019.
W.
Auzinger, M. Fallahpour, O. Koch, E.B. Weinmüller, Implementation
of a pathfollowing strategy with an automatic step-length
control: New MATLAB package bvpsuite2.0, Technical Report
ASC 31/2019.