SPARK3
I have developed the code
spark3.tar.gz
for systems of differential equations, possibly stiff and/or implicit. It
is based on super partitioned additive Runge-Kutta (SPARK) methods.
You can choose between
the Lobatto IIIA-B-C-C*-D coefficients, the Radau IIA coefficients,
and the Gauss coefficients. I have released the version 3.0 on July 16th,
2001.
See the following articles for more theoretical and technical details:
- L.O. Jay:
Preconditioning and parallel implementation of
implicit Runge-Kutta methods.
[.ps.gz].
Submitted.
- L.O. Jay:
Preserving Poisson structure and orthogonality in numerical
integration of differential equations.
[.ps.gz].
Comput. Math. Appl., 2003. To appear.
- L.O. Jay:
Solution of index 2 implicit differential-algebraic equations
by Lobatto Runge-Kutta methods.
[.ps.gz].
BIT, Vol. 43, pp. 91-104, 2003.
- L.O. Jay:
Iterative solution of nonlinear equations for SPARK methods applied to DAEs.
[ .ps.gz,
.pdf.gz].
Numer. Algorithms, Vol. 31, pp. 171-191, 2002.
- L.O. Jay:
Inexact simplified Newton iterations for implicit
Runge-Kutta methods.
SIAM J. Numer. Anal., Vol. 38, pp. 1369-1388, 2000.
[ .ps.gz,
.pdf.gz].
- L.O. Jay and T. Braconnier:
A parallelizable preconditioner for the iterative solution
of implicit Runge-Kutta type methods.
J. Comput. Appl. Math., Vol. 111, pp. 63-76, 1999.
[.pdf.gz].
- L.O. Jay: Structure preservation for constrained dynamics
with super partitioned additive Runge-Kutta methods,
SIAM J. Sci. Comput., Vol. 20, pp. 416-446, 1998.
[ .ps.gz,
.pdf.gz].
Your constructive comments on this code are welcome,
especially any bug reported. Let me add that this code
SPARK3, though it was not Y1K compliant, is
Y2K and even Y3K compliant!
This material is based upon work supported by the National Science
Foundation under Grant No. 9983708.
Any opinions, findings and conclusions or recomendations expressed
in this material are those of the author(s) and do not
necessarily reflect the views of the National Science Foundation (NSF).
Laurent O. Jay
Department of Mathematics
14 MacLean Hall
The University of Iowa
Iowa City, IA 52242-1419
USA
Tel: (319)-335-0898
Fax: (319)-335-0627
E-mail: ljay@math.uiowa.edu
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