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.

Research