Software development for
implicit singular BVPs
Project funded in part by Austrian Sience Foundation (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:
Winfried Auzinger |
Ernst Karner |
Georg Kitzhofer |
Othmar Koch |
Gernot Pulverer |
Christa Simon |
Ewa Weinmüller |
Software:
You can download from here the Matlab package
BVPSUITE and a
manual.
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
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.
G. Kitzhofer, O. Koch, P. Lima, E.
Weinmüller,
Efficient Numerical Solution of the Density Profile
Equation in Hydrodynamics, J. Sci. Comput., 32(2007), pp. 411-424
Ch. Budd, O. Koch, E. Weinmüller, Computation
of Self-Similar Solution Profiles for the Nonlinear Schrödinger Equation,
Computing 77 (2006), pp. 335-346.
Ch. Budd, O. Koch, E. Weinmüller, From
Nonlinear PDEs to Singular ODEs, Appl. Numer. Math.
56(2006), pp. 413-422.
I. Rachunkova, O. Koch, G.
Pulverer, E. B. Weinmüller,
On a
singular boundary value problem arising in the theory of shallow memebrane
caps, Math. Anal. and Appl. 332(2007), pp. 523-541.
S. Stanek, G. Pulverer, E. B.
Weinmüller,
Analysis and numerical solution of positive and dead core solutions of
singular two-point boundary value problems, Comp. Math. Appl. 56(2008),
pp. 1820-1837.