Shooting for Singular BVPs in ODEs

Project funded by Austrian Sience Foundation (FWF grant P12507-MAT) from November 1999 until October 2001. 

• Objectives: 
  Our aim was to prepare the theoretical basis for the design of a standard FORTRAN code (based on the shooting idea) for the numerical solution of singular boundary/initial value problems for systems of ODEs with a singularity of the first kind.
   

• People involved in the project:

Winfried Auzinger

Othmar Koch

Peter Kofler

Ewa Weinmüller

• Software: You can download from here the FORTRAN 90 code avalanche.f, its short description, and a comprehensive report on its application in avalanche modeling. 
  

• Important publications:
  
  O. Koch, E. Weinmüller, Analytical and Numerical Treatment of a Singular Initial Value Problem in Avalanche Modeling, to appear in Applied Mathematics and Computation.
  
  O. Koch, E. B. Weinmüller: The Convergence of Shooting Methods for Singular BVPs, Math. Comp. 72 (2003), no. 241, pp. 289-305.
  
  O. Koch, E. B. Weinmüller, Acceleration Techniques for Singular Initial Value Problems, N. Mastorakis (Ed.),Problems in Modern Applied Mathematics, World Scientific and Engineering Society Press, 2000.
  
  O. Koch, E. B. Weinmüller, Iterated Defect Correction for the Solution of Singular IVPs, SIAM, J. Numer. Anal. 38 (2001), pp. 1784-1799.
  
  O. Koch, P. Kofler, E. B. Weinmüller, The Implicit Euler Method for the Numerical Solution of  Singular Initial Value Problems, Appl. Num. Math. 34 (2000), pp. 231--252.
  
  O. Koch, P. Kofler, E. B. Weinmüller, Initial Value Problems for Systems of Ordinary First and Second Order Differential Equations with a Singularity of the First Kind, Analysis 21 (2001), pp. 373-389.

Research