Software development for implicit singular BVPs
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:
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
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.