PUBLICATIONS
Dr. Graeme Fairweather, Professor and Head
Mathematical and Computer Sciences
Colorado School of Mines
Book and Book Contributions

Finite Element Galerkin Methods for Differential Equations, Lecture Notes
in Pure and Applied Mathematics, Volume 34, Marcel Dekker, New York, 1978,
280 pages.

A. R. Mitchell: Some Biographical and Mathematical Notes,
in Numerical Analysis A. R. Mitchell 75th Birthday Volume, D. F. Griffiths
and G. A. Watson, editors, World Scientific London, 1996, pp. 18, (with
D. F. Griffiths, G. A. Watson and J. D. Lambert).

Preface, Interactive Mathematics Program Year 3, Key Curriculum Press,
Berkeley, California, 1999.
Edited Conference Proceedings

Numerical Integration:
Recent Developments, Software and Applications, Proceedings of the
NATO Advanced Research Workshop, Dalhousie University, Halifax, Nova
Scotia,
August 1115, 1986, D. Reidel Publishing Company, Dordrecht,
The Netherlands, 1987, 394 pages,
(coedited with
P. Keast).

Proceedings of the Workshop on the Method of Lines for Time Dependent
Problems, University of Kentucky, 1995, Appl. Numer. Math., 20(12), 1996,
244 pages, (coedited with I. Gladwell).

Proceedings of the NSF/CBMS Regional Workshop on Hamiltonian
Differential Equations, Colorado School of Mines, 1997, Appl. Numer.
Math.,
29, 1999, 165 pages,
(coedited with I. Gladwell, B. Leimkuhler, E. S. Van Vleck).
Refereed Papers

Improved forms of the alternating direction methods of Douglas, Peaceman
and
Rachford for solving parabolic and elliptic equations, Numer. Math.,
6(1964),
285292, (with A. R. Mitchell).

A generalized alternating direction method of DouglasRachford type for
solving the biharmonic equation, Comput. J., 7(1964), 242245, (with
A. R. Mitchell).

A new alternating direction method for parabolic equations in three space
variables, J. Soc. Indust. Appl. Math., 13(1965),
957965, (with A. R. Mitchell).

A high accuracy alternating direction method for the wave equation,
J. Inst. Math. Appl., 1(1965), 309316, (with A. R. Mitchell).

Some computational results of an improved ADI method for the Dirichlet
problem,
Comput. J., 9(1966), 298303, (with A. R. Mitchell).

Some stable difference approximations to a fourth order parabolic
differential equation, Math. Comp., 10(1967), 111, (with A. R. Gourlay).

Some high accuracy difference schemes with a splitting operator for
equations of parabolic and elliptic type, Numer. Math., 10(1967), 5666,
(with A. R. Gourlay and A. R. Mitchell).

A new computational procedure for A.D.I. methods, SIAM J. Numer. Anal.,
4(1967), 163170, (with A. R. Mitchell).

A note on a generalization of a method of Douglas, Math. Comp., 23(1969),
407409.

Modified Romberg Quadrature, Algorithm 351, Comm. ACM, 12(1969), 324325.

On the eigenvalues and eigenvectors of a class of Hessenberg matrices,
SIAM Rev., 13(1971), 220221.

A survey of discrete Galerkin methods for parabolic equations in one space
variable, Math. Colloq. Univ. Cape Town, 7 (19711972), 4377.

Galerkin methods for vibration problems in two space variables, SIAM J.
Numer.
Anal., 9(1972), 702714.

Three level Galerkin methods for parabolic equations, SIAM. J. Numer.
Anal.,
11(1974), 392410, (with T. Dupont and J. P. Johnson).

Alternating direction Galerkin methods for parabolic and hyperbolic
problems
on rectangular polygons, SIAM J. Numer. Anal., 12(1975), 144163, (with
J. E. Dendy).

On the extrapolation of Galerkin methods for parabolic problems, Numer.
Math.,
23(1975), 269287, (with J. P. Johnson).

A note on the efficient implementation of certain Pad\'e methods for
linear
parabolic problems, BIT, 18(1978), 106109.

An investigation of Romberg quadrature, ACM Trans. Math. Software,
4(1978), 316322, (with P. Keast).

On the numerical solution of twodimensional potential problems by an
improved boundary integral equation method, J. Comput. Phys.,
31(1979), 96112, (with F. J. Rizzo, D. J. Shippy and Y. S. Wu).

On the approximate solution of a diffusion problem by Galerkin methods,
J. Inst. Math. Appl., 24(1979), 121137.

A linear ADI method for the shallow water equations, J. Comput. Phys.,
36(1980), 118, (with I. M. Navon).

Annular bed reactor  methanation of carbon dioxide, Can. J. Chem. Eng.,
59(1981), 497500, (with M. Davis and J. Yamanis).

On the use of spline collocation for boundary value problems arising in
chemical engineering, Comput. Methods Appl. Mech. Engrg., 18(1981),
179189, (with M. Davis).

Analysis of SO^{2} oxidation in nonisothermal catalyst pellets using the
dustygas model, Chem. Eng. Sci., 37(1982), 447452, (with M. Davis and
J. Yamanis).

A computational study of finite element methods for second order twopoint
boundary value problems, Math. Comp., 40(1983), 499518, (with P. Keast
and
J. C. Diaz).

Solution of boundary value problems using software packages: DD04AD and
COLSYS, Chem. Eng. Commun., 22(1983), 19, (with K. S. Denison and
C. E. Hamrin, Jr.).

The effect of Prandtl number on heat transfer from a rotating disk with
blowing at the wall, Int. Comm. Heat Mass Transfer,
10(1983), 287297, (with P. H. Muir and M. VedhaNayagam).

Fortran packages for solving certain almost block diagonal systems by
modified
alternate row and column elimination, ACM Trans. Math. Software,
9(1983), 358375,
(with J. C. Diaz and P. Keast).

Algorithm 603 COLROW and ARCECO:
Packages for solving certain almost block diagonal linear systems by
modified
alternate row and column elimination,
ACM Trans. Math. Software, 9(1983), 376380,
(with J. C. Diaz and P. Keast).

On the application of extrapolation, deferred correction and defect
correction
to discretetime Galerkin methods for
parabolic problems, IMA J. Numer. Anal.,
3(1983), 173192, (with A. V. Saylor).

The noniterative solution of nonlinear parabolic and mixedtype problems
arising in reactor design, Chem. Eng. Commun., 23(1983), 8999,
(with M. E. Davis
and J. Yamanis).

On the H^{1}Galerkin method for secondorder linear twopoint
boundary value problems, SIAM J. Numer. Anal., 21(1984), 314326,
(with P. Keast and J. C. Diaz).

A note on the condition of a matrix, Int. Comm. Heat Mass Transfer,
11(1984), 191195.

The method of fundamental solutions for problems
in fluid flow,
Appl. Math. Modeling, 8(1984), 265270, (with R. L. Johnston).

A survey of higher order methods for
the numerical integration of semidiscrete parabolic problems,
IMA J. Numer. Anal., 4(1984), 375425, (with W. L. Seward and
R. L. Johnston).

Letter to the Editor, A.I.Ch.E.J., 31(1985), 351352, (with C. P. Kelkar
and
C. E. Hamrin, Jr.).

Prediction of membrane separation characteristics by pore distribution
measurements
and surface forcepore flow model, Chem. Eng. Commun.,
42(1986), 111128, (with
D. Bhattacharyya,
M. Jevtitch and J. T. Schrodt).

Analyses of spline collocation methods for parabolic and hyperbolic
problems in two space variables, SIAM J. Numer. Anal., 23(1986),
282296, (with
C. E. GreenwellYanik).

On the asymptotic expansion of the discretization error of certain
discretetime
Galerkin methods for parabolic problems, Numer. Funct. Anal. Optim.,
8(198586),
447471,
(with A. V. Saylor).

Reformulation and the numerical solution of the equations for a catalytic,
porous wall, gasliquid reactor, Computers Chem. Eng., 10(1986), 361365,
(with
A. Akyurtlu,
J. F. Akyurtlu
and C. E. Hamrin, Jr.).

The method of fundamental solutions for the numerical solution of
the biharmonic
equation,
J. Comput. Phys., 69(1987), 434459, (with A. Karageorghis).

An assessment of numerical software for solving twopoint boundary
value problems arising in heat transfer, Numerical Heat Transfer,
11(1987),
281293, (with
M. VedhaNayagam).

The effect of surface mass transfer on buoyancyinduced flow in a
variableporosity
medium adjacent to a horizontal heated plate, Int. Comm. Heat Mass
Transfer, 14(1987), 495506,
(with M. VedhaNayagam and P. Jain).

Numerical simulation of transport from an infinite line source: error
analysis,
Atmos. Environ., 22(1988), 7582, (with P. S. Kasibhatla and
L. K. Peters).

The Almansi method of fundamental solutions for solving biharmonic
problems,
Internat. J. Numer. Methods Engrg., 26(1988), 16651682, (with A.
Karageorghis).

Finite element methods for parabolic and hyperbolic partial
integrodifferential
equations, Nonlinear Anal., 12(1988), 785809, (with E. G. Yanik).

The method of fundamental solutions for the solution of nonlinear plane
potential problems, IMA J. Numer. Anal., 9(1989), 231242,
(with A. Karageorghis).

A survey of spline collocation methods for the numerical solution of
differential equations,
Mathematics for Large Scale Computing, J. C. Diaz, ed., Lecture Notes
in Pure and Applied Mathematics, Volume 120, Marcel Dekker,
New York, 1989, pp. 297341,
(with D. Meade).

The simple layer potential method of fundamental solutions
for certain biharmonic problems, Internat. J. Numer. Methods Fluids,
9(1989), 12211234,
(with A. Karageorghis).

On the numerical solution of a model air pollution problem with nonsmooth
initial data,
Comm. Appl. Numer. Methods, 6(1990), 145156,
(with W. L. Seward and P. Kasibhatla).

A stabilized Galerkin method for a third order evolutionary problem, Math.
Comp., 55(1990), 497507,
(with J. M. SanzSerna and I. Christie).

The reformulation and numerical solution of certain nonclassical
initialboundary value problems, SIAM J. Sci. Statist. Comput.,
12(1991), 127144, (with R. D. Saylor).

An alternating direction Galerkin method for a class of second order
hyperbolic equations in two space variables,
SIAM J. Numer. Anal., 18(1991), 12651281,
(with R. I. Fernandes).

A box method for a nonlinear equation of population dynamics,
IMA J. Numer. Anal., 11(1991), 525538, (with J. C. LópezMarcos).

On the use of the software package SPRINT in the study of
atmospheric turbulence in a convective boundary layer,
Environmental Software, 6(1991), 120130,
(with P. Pai and T. H. Tsang).

Fast direct solvers for piecewise Hermite bicubic orthogonal
spline collocation equations,
SIAM J. Numer. Anal., 29(1992), 156173,
(with B. Bialecki and K. R. Bennett).

Analysis of acoustic scattering in fluids and solids by the method of
fundamental solutions, J. Acoust. Soc. Amer.,
91(1992), 18441854,
(with D. J. Shippy and
P. S. Kondapalli).

The method of fundamental solutions for transmission and scattering of
elastic
waves,
Comput. Methods Appl. Mech. Engrg., 96(1992), 255269,
(with D. J. Shippy and P. S. Kondapalli).

Orthogonal spline collocation methods for some partial integrodifferential
equations, SIAM J. Numer. Anal., 29(1992), 755768,
(with Y. Yan).

The solution of almost block diagonal linear systems arising in spline
collocation
at Gaussian points with monomial basis functions,
ACM Trans. Math. Software, 18(1992), 193204,
(with F. Majaess, P. Keast and K. R. Bennett).

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,
ACM Trans. Math. Software, 18(1992), 205210,
(with F. Majaess, P. Keast and K. R. Bennett).

A parallel boundaryvalue ODE code for sharedmemory machines,
Internat. J. High Speed Computing, 4(1992), 7186,
(with K. R. Bennett).

On the numerical solution of the cubic
Schrödinger
equation in one space
variable, J. Comput. Phys., 103(1993), 277284,
(with M. P. Robinson and B. M. Herbst).

Analysis of alternating direction collocation methods for parabolic and
hyperbolic problems in two space variables, Numerical Methods for Partial
Differential Equations, 9(1993), 191211,
(with R. I. Fernandes).

Matrix decomposition algorithms for separable elliptic boundary value
problems in two space dimensions, J. Comput. Appl. Math., 46(1993),
369386,
(with B. Bialecki).

A fourthorder cubic spline method for linear secondorder twopoint
boundary value problems,
IMA J. Numer. Anal., 13(1993), 591607,
(with I. H. Sloan and Dat Tran).

Orthogonal cubic spline collocation solution of
underwater acoustic wave propagation problems, J. Comput. Acoust.,
1(1993), 355370,
(with M. P. Robinson).

An explicit extrapolated box scheme for the GurtinMacCamy equation,
Comput. Math. Appl., 27(1994), 4153,
(with J. C. LópezMarcos).

Fourier methods for piecewise Hermite bicubic orthogonal spline
collocation, EastWest J. Numer. Math., 2(1994), 120,
(with B. Bialecki and K. A. Remington).

Spline collocation methods for a class of hyperbolic
partial integrodifferential equations,
SIAM J. Numer. Anal., 31(1994), 444460.

Orthogonal spline collocation methods for
Schrödingertype
equations in one space variable, Numer. Math., 68(1994), 355376,
(with M. P. Robinson).

The current state and future direction of Eulerian models in simulating
the tropospheric chemistry and transport of trace species: a review,
Atmospheric Environment, 28(1995), 189222,
(with L. K. Peters, C. M. Berkowitz, G. R. Carmichael,
R. C. Easter, S. T. Ghan, J. M. Hales,
L. R. Leung, W. R. Pennell, F. A. Potra, R. D. Saylor, and T. T. Tsang).

Matrix decomposition algorithms in orthogonal spline collocation
for separable elliptic boundary value
problems, SIAM J. Sci. Comput., 16(1995), 330347, (with
B. Bialecki).

Diffusion flame over a continuous moving fuel plate in a parallel flow of
oxidizer under microgravity, AIAA
J. Thermophysics and Heat Transfer, 10(1996), 97101,
(with M. VedhaNayagam).

Spline collocation calculation for the hydrogen molecular ion,
J. Physics B: At. Mol. Opt. Phys., 29(1996), 23752391,
(with J. C. Morrison, C. Baunach, L. Larson and
B. Bialecki).

Galerkin methods for a semilinear parabolic problem with nonlocal boundary
conditions, Adv. Comput. Math., 6(1996), 243262,
(with J. C. LópezMarcos).

Discretetime orthogonal spline collocation methods for
Schrödinger
equations in two space variables, SIAM J. Numer. Anal., 35(1998), 453477,
(with B. Li and B. Bialecki).

Orthogonal spline collocation methods for biharmonic problems,
Numer. Math., 80(1998), 267303, (with Z. Lou and B. Bialecki).

The method of fundamental solutions for elliptic boundary value
problems, Adv. Comput. Math., 9(1998), 6995,
(with A. Karageorghis).

The method of fundamental solutions for axisymmetric acoustic scattering
and radiation problems,
J. Acoust. Soc. Am., 104(1998), 32123218,
(with A. Karageorghis).

The method of fundamental solutions for axisymmetric potential problems,
Internat. J. Numer. Methods Engrg., 44(1999), 16531669,
(with A. Karageorghis).

A CrankNicolson orthogonal spline collocation method for vibration
problems, Appl. Numer. Math., 33(2000), 299306, (with B. Li and B.
Bialecki).

The method of fundamental solutions for axisymmetric elasticity problems,
Computational Mechanics, 25(2000) 524532, (with A. Karageorghis).

Almost block diagonal linear systems: sequential and parallel solution
techniques
and applications, Numer. Linear Algebra
Appl., 7(2000) 275317, (with P. Amodio, J. R. Cash, G. Roussos,
R. W. Wright, I. Gladwell, G. L. Kraut and M. Paprzycki).

Numerical solutions of the orbital equations for diatomic molecules,
Molecular Physics, 98 (2000), 11751184, (with J. C. Morrison, T. Wolf,
B. Bialecki and L. Larson).

Orthogonal spline collocation methods for partial differential equations,
J. Comput. Appl. Math., 128(2001), 5582, (with B. Bialecki).

Numerical methods for Schrodingertype problems, in "Trends in
Industrial and Applied Mathematics", A. H. Siddiqi and M. Kocvara,
editors, Kluwer Academic Publishers, Boston, 2002, pp. 219250, (with M.
Khebchareon).

H^{1}Galerkin mixed finite element methods for parabolic partial
integrodifferential equations, IMA J. Numer.Anal., 22(2002), 231252,
(with A. Pani).

Discretetime orthogonal spline collocation methods for vibration
problems, SIAM J. Numer. Anal., 39(2002), 20452065, (with B. Li and B.
Bialecki).

Matrix decomposition algorithms for modified spline collocation for
Helmholtz problems, SIAM J. Sci. Comput., 24(2003), 17331753, (with B.
Bialecki and A. Karageorghis).

An H^{1}Galerkin mixed finite element method for an evolution equation
with a positive type memory term, SIAM J. Numer. Anal., 40 (2003),
14751490, (with A. Pani).

The method of fundamental solutions for scattering and radiation problems,
Engineering Analysis with Boundary Elements, 27 (2003), 759769,
(with A. Karageorghis and P. A. Martin).

Algorithms for almost block diagonal linear systems, SIAM Rev., 46(2004), 4958,
(with I. Gladwell).

A matrix decomposition MFS algorithm for axisymmetric biharmonic problems,
Adv. Comput. Math, 23(2005), 5571, (with Y.S. Smyrlis and A. Karageorghis).

Optimal superconvergent one step cubic spline collocation methods,
SIAM J. Sci. Comput., 27(2005), 575598, (with B. Bialecki and A. Karageorghis).

Asymptotic expansions and Richardson extrapolation of approximate solutions for
second order elliptic problems on rectangular domains by mixed finite element
methods, SIAM J. Numer. Anal., 44 (2006), 11221149, (with Q. Lin, Y. Lin, J.
Wang and S. Zhang).

Potential field based geometric modeling using the MFS,
Internat. J. Numer. Methods Engrg., 68 (2006), 12571280, (with Y. S. Smyrlis, A.
Karageorghis and R. Tankelevich).
Papers in Refereed Conference Proceedings

The method of fundamental solutions for problems in potential theory,
Treatment of Integral Equations by Numerical Methods,
C. T. H. Baker and
G. F. Miller, editors, Academic Press, London, 1982, 349359,
(with R. L. Johnston).

On the use of numerical software for solving twopoint boundary value
problems arising in heat transfer,
AIChE/ASME 23rd
National Heat Transfer Conference, Denver, Colorado, August 1985, (with M.
VedhaNayagam).

Packages for solving almost block diagonal linear systems arising
in spline collocation at Gaussian points with monomial basis functions,
Scientific Software Systems, J. C. Mason and M. G. Cox, editors,
Chapman and Hall, London, 1990, 4758,
(with
F. Majaess and P. Keast).

An orthogonal spline collocation method for the numerical solution
of underwater acoustic wave propagation problems,
Computational Acoustics  Volume 2, D. Lee, A. R. Robinson and
R. Vichnevetsky, editors, Elsevier Science Publishers, Amsterdam,
1993,
pp. 339353,
(with M. P. Robinson).

An additive Schwarz algorithm for piecewise Hermite bicubic
orthogonal spline collocation, Proceedings of the
Sixth International Conference on Domain Decomposition Methods
in Science and Engineering, Contemporary Mathematics,
Vol. 157,
American Mathematical Society,
Providence, RI, 1994, pp. 237244,
(with B. Bialecki, X.C. Cai and M. Dryja).
Questions/comments to: gfairwea@mines.edu
October 2003