Software development for explicit singular BVPs in ODEs

Project funded by the Mathematics department at TU Wien January 2000 - December 2002 and by Austrian Sience Foundation (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:

Winfried Auzinger

Günter Kneisl

Othmar Koch

Ewa Weinmüller

• Software: You can download (via the MathWorks homepage) the package SBVP1.0, a manual and a comprehensive report on the performance of the code. 
  

• Important publications:
  
  W. Auzinger, O. Koch, E. B. Weinmüller: Efficient Collocation Schemes for Singular Boundary Value Problems, Numer. Algorithms 31(2002), pp. 5-25.
  
  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.
  
  W. Auzinger, O. Koch, E. Weinmüller, Analysis od a New Error Estimate for Collocation Methods Applied to Singular Boundary Value Problem, SIAM, J. Numer. Anal. 42(2005), pp. 2366-2386.
  
  W. Auzinger, O. Koch, E. Weinmüller, Efficient Mesh Selection for Collocation Methods Applied to Singular BVPs, J. Comput. Appl. Math. 1, Vol. 180(2005), pp. 213-227.

Research