Math related links:

MathSciNet
The Fields Institute
Society for Industrial and Applied Mathematics
Canadian Mathematical Society
Canadian Applied and Industrial Mathematical Society
American Mathematical Society
NETLIB

Publications:

[1] A comparison of adaptive software for 1-D parabolic PDEs, Rong Wang, Patrick Keast and Paul H. Muir , J. Comput. Appl. Math., Vol 169, 2004, pp. 127-150.

[2] A high-order global spatially adaptive collocation method for 1-D parabolic PDEs, Rong Wang, Patrick Keast and Paul H. Muir , Appl. Numer. Math., Vol 50, 2004, pp. 239-260.

[3] BACOL: B-spline Adaptive COLlocation software for 1-D parabolic PDEs, Rong Wang, Patrick Keast and Paul H. Muir , ACM Trans. Math. Softw., Vol 30, 2004, pp. 454-470.

[4] Linear instability of the fifth-order WENO method, Rong Wang and Raymond J. Spiteri , SIAM J. Numer. Anal., Vol 45, 2007, pp. 1871-1901.

[5] Algorithm 874: BACOLR: Spatial and Temporal Error Control Software for PDEs based on High Order Adaptive Collocation, Rong Wang, Patrick Keast and Paul H. Muir , to appear in ACM Trans. Math. Softw.

[6] Observations on the fifth-order WENO method with non-uniform meshes, Rong Wang, Hui Feng, and Raymond J. Spiteri , Appl. Math. Comput., Vol 196, 2008, pp. 433-447.

[7] Stability barrier for the seventh-order WENO method, Rong Wang and Raymond J. Spiteri , submitted to SIAM J. Numer. Anal..

[8] Linear stability analysis of the ninth- and eleventh-order WENO methods, Rong Wang and Raymond J. Spiteri , submitted to Math. Comp..

Technique Reports:

[1] Saint Mary's University Mathematics and Computing Science Technical Report 2005-003, Collocation software based on a Runge-Kutta time integrator for 1-D parabolic PDEs and Schrodinger type problems, with spatial and temporal error control, Rong Wang, Patrick Keast and Paul H. Muir .

Software:
BACOL is a high quality, robust software package in Fortran 77 for solving one-dimensional parabolic PDEs. It employs high order, adaptive methods in both time and space, controlling and balancing spatial and temporal error estimates. The software implements a spline collocation method at Gaussian points, with a B-spline basis, for the spatial discretization. The time integration is performed using a modification of the popular DAE solver, DASSL. Based on the computation of a second, higher order, global solution, a high quality a posteriori spatial error estimate is obtained after each successful time step. The spatial error is controlled by a sophisticated new mesh selection algorithm based on an equidistribution principle. Two examples are provided to illustrate the use of the package. Example 1 is for a single equation, while Example 2 is for a PDE system with 4 components.

BACOLR is an extension of BACOL by use a RK solver RADAU5 instead of the BDF solver DASSL. BACOLRNOBLAS includes subroutines of BACOLR without any BLAS routines, and BLASSUB includes all the BLAS subroutines used by BACOLR. Example 3 is for a single equation, while Example 4 is for a PDE system with 4 components.