BVPSUITE 2.0 (2020)

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:

Software:
You can download from here the Matlab package BVPSUITE2.0, öffnet eine Datei in einem neuen Fenster 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  ewa.weinmueller@tuwien.ac.at

Important publications:

[1] O. Koch, Asymptotically Correct Error Estimation for Collocation Methods Applied to Singular Boundary Value Problems, öffnet eine externe URL in einem neuen Fenster, Numer. Math. 101(2005), pp. 143–164.

[2] W. Auzinger, E. Karner, O. Koch, E. B. Weinmüller, Collocation Methods for the Solution of Eigenvalue Problems for Singular Ordinary Differential Equations, öffnet eine Datei in einem neuen Fenster, Opuscula Math. 26/2(2006), pp. 229–241.

[3] G. Kitzhofer, O. Koch, E. B. Weinmüller, Pathfollowing for Essentially Singular Boundary Value Problems with Application to the Complex Ginzburg-Landau Equation, öffnet eine Datei in einem neuen Fenster, BIT Numer. Math. 49(2009), pp. 217–245.

[4] G. Pulverer, G. Söderlind, E. Weinmüller, Automatic Grid Control in Adaptive BVP Solvers, öffnet eine Datei in einem neuen Fenster, Numer. Algorithms 56(2011), pp. 61–92.

[5] W. Auzinger, O. Koch, E.B. Weinmüller, S. Wurm, Modular version bvpsuite1.2 of the collocation MATLAB package bvpsuite1.1, öffnet eine Datei in einem neuen Fenster, Technical Report ASC 30/2019.

[6] 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, öffnet eine Datei in einem neuen Fenster, Technical Report ASC 31/2019.

 

BVPSUITE 1.1 (2010)

Project funded in part by Austrian Sience Foundation, öffnet eine externe URL in einem neuen Fenster (FWF grant P17253-N12)  from October 2004 until October 2006.

Objectives: 
Our aim is to provide a MATLAB code (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 aim for the full theoretical justification of the code components, collocation solver, errror estimation procedure and grid adaptation strategy.

Members of the Research Group "Numerics and Simulation of Differential Equations"  involved in the project:

Software:

You can download from here the Matlab package BVPSUITE, öffnet eine Datei in einem neuen Fenster and a manual., öffnet eine Datei in einem neuen Fenster This version BVPSUITE1.1 (Release July 2010) is optimized for the Matlab Versions 7.1–7.2 (R2006a) and tested with the Matlab Versions R2007b (under Windows), R2008b (under Windows) R2009b (under Windows and Unix). The code should also work for later versions of Matlab. The software can be used under the conditions of the licence enclosed in the zip-file containing the code. If you have suggestions or remarks concerning BVPSUITE, please contact us at  ewa.weinmueller@tuwien.ac.at

Important publications:

[1]–[4]

[7] G. Kitzhofer, O. Koch, P. Lima, E. Weinmüller, Efficient Numerical Solution of the Density Profile Equation in Hydrodynamics, öffnet eine Datei in einem neuen Fenster, J. Sci. Comput., 32(2007), pp. 411–424

[8] Ch. Budd, O. Koch, E. Weinmüller, Computation of Self-Similar Solution Profiles for the Nonlinear Schrödinger Equation, öffnet eine Datei in einem neuen Fenster, Computing 77 (2006), pp. 335–346.

[9] Ch. Budd, O. Koch, E. Weinmüller, From Nonlinear PDEs to Singular ODEs, öffnet eine Datei in einem neuen Fenster, Appl. Numer. Math. 56(2006), pp. 413–422.

[10] I. Rachunkova, O. Koch, G. Pulverer, E. B. Weinmüller, On a singular boundary value problem arising in the theory of shallow membrane caps, öffnet eine Datei in einem neuen Fenster, Math. Anal. and Appl. 332(2007), pp. 523–541.

[11] S. Stanek, G. Pulverer, E. B. Weinmüller, Analysis and numerical solution of positive and dead core solutions of singular two-point boundary value problems, öffnet eine Datei in einem neuen Fenster, Comp. Math. Appl. 56(2008), pp. 1820–1837.

Project funded by the Mathematics department at TU Wien, öffnet eine externe URL in einem neuen Fenster January 2000 to December 2002 and by Austrian Sience Foundation, öffnet eine externe URL in einem neuen Fenster (FWF grant P15072)  from November 2002 until October 2003.

Objectives: 
Our aim is to provide a MATLAB code (based on collocation) for the numerical solution of singular boundary value problems for systems of ODEs with a singularity of the first and second kind.

Members of the Department involved in the project:

Software:
You can download (via the MathWorks homepage) the package SBVP1.0, öffnet eine Datei in einem neuen Fenster, a manual, öffnet eine Datei in einem neuen Fenster and a comprehensive report, öffnet eine Datei in einem neuen Fenster on the performance of the code. 

Important publications:

  • W. Auzinger, G. Kneisl, O. Koch, E. B. Weinmüller: A Solution Routine for Singular Boundary Value Problems, Technical Report, ANUM Preprint 1/02, 2002.
  • W. Auzinger, G. Kneisl, O. Koch, E. B. Weinmüller: A Collocation Code for Boundary Value Problems in Ordinary Differential Equations, Numer. Algorithms, 33(2003), pp. 27–39.