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.