- Algorithm 874: BACOLR: Spatial and Temporal Error Control Software for PDEs based on High Order Adaptive Collocation.
Wang, Pat Keast
and Paul H. Muir. This is available
as a technical
report. The software and two driving programs are available
on the web. (To appear in
ACM Transactions on Mathematical Software, volume 34, no. 3, (2008).)
- A comparison of adaptive software for 1-D parabolic PDEs,
and Paul H. Muir,
J. Comput. Appl. Math., 169 (2004), 127-150.
pdf form, and
- A high-order global spatially adaptive collocation method for 1-D parabolic PDEs,
Pat Keast and Paul H. Muir,
Appl. Numer. Math., 50 (2004), 239-260.
pdf form, and
- BACOL: B-spline Adaptive COLlocation software for 1-D parabolic PDEs,
Pat Keast and Paul H. Muir,
ACM Trans. Math. Soft., 30 (2004), 454-470. Available in
pdf form, and ps form.
The software can be obtained here.
- Pulse Detection software for Initial Value ODEs, with Amy
Hynick and Paul H. Muir,
Mathematical and Computer Modelling, 40 (2004), 1335-1350.
The source code, together with lsode on which it is based, and a sample
driver are available in the directory pulse. The files
may be downloaded separately or in tarred and gzip form in
A sinc quadrature subroutine for cauchy principal value integrals, with B.
J. Comput. and Appl. Math., 112 (1999), 3-20. The code is
in the file sinc.f .
A method of lines package, based on monomial spline collocation, for systems
of one dimensional parabolic differential equations, with T.B. Nokonechny
and P. Muir, Numerical Analysis, (A.R. Mitchell 75th birthday volume), World
Scientific Publishing, (1996), 207--224.
Applications of the Smith Normal Form to lattice integration rules,
with J.N. Lyness, SIAM J. Matrix Analysis and Applications, 16
The solution of almost block diagonal linear systems arising in spline
collocation at Gaussian points with monomial basis functions,
with F. Majaess, G. Fairweather, and K. Bennett, ACM Trans. on Math. Software,
18 (1992), 193-204.
Algorithm 704: ABDPACK and ABBPACK - Fortran programs for the solution
of almost block diagonal linear systems arising in spline collocation
at Gaussian points with monomial basis functions, with F. Majaess,
and K. Bennett, ACM Trans. Math. Software, 18 (1992), 205-210.
(Available as TOMS/704.)
EPDCOL : A more efficient PDECOL code, with P.H.
Muir, ACM Trans. on
Math. Software, 17 (1991), 153-166.
(Available as TOMS/688.)
A sample driver is available here, and the double precision version
is in the file pdecoldp.f.
Notes on Integration and Integer Sublattices, with J.N. Lyness and
T. Sorevik, Math of Comp, 56 (1991), 243--256.
The directory leq contains some unpublished software for solving almost block
diagonal linear systems, tridiagonal systems and block tri-diagonal systems.
complexcolrow.f is a
complex version of the software package COLROW, available as
TOMS/603 at netlib.
The double precision
complex version is in complexcolrowd.f.
colrow.f is a modified version of COLROW which
can solve the system ATx = 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 TOMS/674. The condition
umber estimator is given in condcolrow.f
Matlab versions of the colrow codes and the condition number estimator
can be found in colrowm . These were written
as part of an MSc thesis by Rania Ghanam, Dalhousie University, January
The code lampak.f is an alternative approach
to the factorization of almost block diagonal systems.
The package ABDPACK, (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 ATx = b.
This modified software, and the subroutine DONEST (a double precision version
of TOMS/674) is in
abdcnd.f. A short report on this work is
in a technical report.
This package was developed by an Honours student,
Roderick Alexander Affleck, BSc 1997, for his Honours thesis
Condensation of Almost Block Diagonal
Matrices in Monomial Spline Collocation of Parabolic Differential Equations.
The block-tridiagonal codes are in the sub-directory block-tri-diag.
Some related work on tridiagonal systems by
Graeme Fairweather can be found here.