Selected Publications

• Algorithm 874: BACOLR: Spatial and Temporal Error Control Software for PDEs based on High Order Adaptive Collocation. Rong 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, Rong Wang, Pat Keast and Paul H. Muir, J. Comput. Appl. Math., 169 (2004), 127-150. Available in pdf form, and postscript form.

• 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. Available in pdf form, and postscript form.

• 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. 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 pdode.tar.gz.

• A sinc quadrature subroutine for cauchy principal value integrals, with B. Bialecki, J. Comput. and Appl. Math., 112 (1999), 3-20. The code is available here, 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 (1995), 218-231.

• 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, G. Fairweather 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.

Unpublished Software

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 A^Tx = 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 2007.

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 A^Tx = 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.