A comparison of adaptive software for 1-D parabolic PDEs,
Rong Wang,
Pat Keast
and Paul H. Muir,
J. Comput. Appl. Math., 169 (2004), 127-150.
A high-order global spatially adaptive collocation method for 1-D parabolic PDEs,
Rong Wang,
Pat Keast and Paul H. Muir,
Appl. Numer. Math., 50 (2004), 239-260.
BACOL: B-spline Adaptive COLlocation software for 1-D parabolic PDEs,
Rong Wang,
Pat Keast and Paul H. Muir,
ACM Trans. Math. Soft., 30 (2004), 454-470.
Pulse Detection in Initial Value ODEs, with Amy
Hynick and Paul H. Muir,
Mathematical and Computer Modelling, 40 (2004), 1335-1350.
Unpublished Software:
These packages are all available in the directory
http://www.mathstat.dal.ca/~keast/research/pubs.html .
(i) complexcolrow.f is a complex version of the software package COLROW,
TOMS algoritthm 603 at http://www.netlib.org/.
The double precision
complex version is used in the software in the paper on BACOLR, above.
(ii) colrow.f is a modified version of COLROW which
can solve the system A^T x = b, after first performing the Gauss
Factorization of A, using the same algorithm as COLROW. This facilitates
a condition number estimation, using the procedure of Nick Higham,
in http://www.netlib.org/toms/674. The condition
number estimator is given in condcolrow.f . This has been used extensively in
tests on the codes BACOLR, BACOL and MSCPDE, in the above paper with Muir and
Nokonechny.
(iii) The code lampak.f is an alternative approach
to the factorization of almost block diagonal systems.
(iv) The package ABDPACK, in www.netlib.org/toms/704>,
solves systems of the form Ax = b, where A has a special structure arising
from collocation at Gauss points. In order to provide a way of estimating
the condition number of A the code was modified to handle A^{T}x = b.
This modified software uses the subroutine DONEST (a double precision version
of Higham's code (above, (ii)).
This package was developed with an Honours student,
Roderick Alexander Affleck, BSc (CS) 1997, for his Honours thesis,
Condensation of Almost Block Diagonal
Matrices in Monomial Spline Collocation of Parabolic Differential Equations.
(v) Block-tridiagonal codes are in the sub-directory leq/block-tri-diag>.