Publications
(many available in Postscript
and PDF
formats):
Publications in peerreviewed journals:

Analytical Upstream Collocation Solution of a Quadratically
Forced SteadyState
ConvectionDiffusion Equation
by Stephen Brill and Eric Smith
International Journal of Numerical Methods for
Heat and Fluid Flow
Vol. 22, No. 4, pp. 436457, 2012.
Color figures in pdf

Optimal Hermite Collocation Applied to a OneDimensional ConvectionDiffusion
Equation Using an Adaptive Hybrid Optimization Algorithm
by Karen L. Ricciardi and Stephen H. Brill
International Journal of Numerical Methods for
Heat and Fluid Flow,
Vol. 19, No. 7, pp. 874893, 2009.

Optimal Collocation
Solution of the OneDimensional SteadyState ConvectionDiffusion Equation
with Variable Coefficients
by Stephen H. Brill
International Journal of Computational and
Numerical Analysis and Applications, Vol. 6, No. 3, pp. 257283, 2004.

Analytical Upstream Collocation Solution of a Forced
OneDimensional SteadyState ConvectionDiffusion
Equation
by Stephen H. Brill
International Journal of Differential Equations and Applications,
Vol. 7, No. 1, pp. 6999, 2003.

Optimal Upstream Collocation Solution of the
OneDimensional SteadyState ConvectionDiffusion
Equation
by Stephen H. Brill
International Journal of Applied Mathematics,
Vol. 10, No. 2, pp. 197215, 2002.

Analytical Solution of Hermite Collocation Discretization
of SelfAdjoint Ordinary Differential Equations
by Stephen H. Brill
International Journal of Differential Equations and
Applications,
Vol. 6, No. 1, pp. 118, 2002.

Parallel Implementation of the BiCGSTAB Method with
Block RedBlack GaussSeidel Preconditioner Applied
to the Hermite Collocation Discretization of
Partial Differential Equations
by Stephen H. Brill and George F. Pinder
Parallel Computing, Vol. 28, pp. 399414, 2002.

Analytical Solution of Hermite Collocation Discretization
of the SteadyState ConvectionDiffusion Equation
by Stephen H. Brill
International Journal of Differential Equations and
Applications,
Vol. 4, No. 2, pp. 141155, 2002.

Analysis of a Block RedBlack
Preconditioner Applied to the
Hermite Collocation Discretization of
a Model Parabolic Equation
by Stephen H. Brill and George F. Pinder
Numerical Methods for Partial Differential Equations,
Vol. 17, No. 6, pp. 584606, November 2001.

Eigenvalue Analysis of a Block RedBlack
GaussSeidel Preconditioner Applied to the
Hermite Collocation Discretization of
Poisson's Equation
by Stephen H. Brill and George F. Pinder
Numerical Methods for Partial
Differential Equations,
Vol. 17, No. 3, pp. 204228, May 2001.

Hermite Collocation Solution of Partial Differential
Equations via Preconditioned Krylov Methods
by Stephen H. Brill
Numerical Methods for Partial
Differential Equations,
Vol. 17, No. 2, pp. 120136, March 2001.
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Publications in conference proceedings, etc.:

A Family of Solutions for the OneDimensional Transport Equation
by Stephen H. Brill
Proceedings of the
XVI International Conference on
Computational Methods in Water Resources, 2006.

Optimal Collocation Applied to a OneDimensional ConvectionDiffusion
Equation Using a Hybrid Optimization Algorithm
by Karen L. Ricciardi and Stephen H. Brill
Proceedings of the
XVI International Conference on
Computational Methods in Water Resources, 2006.

Optimal Upstream Collocation: A Survey of Recent Results
by Stephen H. Brill
Proceedings of the
XV International Conference on
Computational Methods in Water Resources, 2004.

The Analytical Solution of the Hermite Collocation Discretization
of the OneDimensional SteadyState ConvectionDiffusion Equation:
A Survey of Recent Results
by Stephen H. Brill
INRA/INEEL Subsurface Science Symposium,
2002.

Optimal Hermite Collocation
Solution of a Forced ConvectionDiffusion Equation
by Stephen H. Brill and V.K. Stepanyan
Proceedings of the
XIV International Conference on
Computational Methods in Water Resources, 2002.

Optimal Upstream Collocation Solution of a ConvectionDiffusion Equation
by Stephen H. Brill
INRA/INEEL Subsurface Science Symposium,
2001.

Solving Multiphase Equations from a Dynamical Systems
Point of View
by Stephen H. Brill
Proceedings of the
XIII International Conference on
Computational Methods in Water Resources,
2000.

The BiCGTAB Method with RedBlack
GaussSeidel Preconditioner
Applied to the Hermite Collocation
Discretization
of Subsurface Multiphase Flow and
Transport Problems
by Stephen H. Brill, Joseph F. Guarnaccia,
and George F. Pinder
Proceedings of the
XII International Conference on
Computational Methods in Water Resources,
1998.

Documentation for Collocation Software
by Stephen H. Brill
RCGRD Publication #9801,
Research Center for Groundwater Remediation Design,
University of Vermont, Burlington, Vermont,
1998.

The Solution of TwoDimensional Partial Differential Equations via Hermite
Collocation with Block RedBlack GaussSeidel Preconditioner
by Stephen H. Brill
Ph.D. dissertation,
University of Vermont, Burlington, Vermont,
1998.

A Parallel Preconditioned
BiConjugate Gradient Algorithm
for TwoDimensional Elliptic and Parabolic
Equations Using Hermite Collocation
by Stephen H. Brill and George F. Pinder
Proceedings of the Eighth SIAM Conference
on Parallel Processing for Scientific Computing,
1997.

A Block RedBlack SOR Method for a TwoDimensional
Parabolic Equation Using Hermite Collocation
by Stephen H. Brill and George F. Pinder
The Mathematics of Finite Elements
and Applications
John Wiley & Sons Ltd., 1997.
This page was most recently updated on 30 May 2013.