\bibitem{Boyle-Caviness}
A. Boyle and B.F. Caviness, Editiors,
{\em Future Directions for Research in Symbolic Computing},
SIAM, Philadelphia, 1989

\bibitem{ISSAC89}
G.H. Gonnet, Editor,
{\em ISSAC '89, Proceedings of the International Symposium on
Symbolic and Algebraic Computation},
ACM-Press, New York, 1989.

\bibitem{ISSAC90}
S. Watanabe and M. Nagata, Editors,
{\em ISSAC '90, Proceedings of the International Symposium on
Symbolic and Algebraic Computation},
ACM Press, Addison Wesley, New York, 1990.

\bibitem{ISSAC91}
S.M. Watt, Editor,
{\em ISSAC '91, Proceedings of the International Symposium on
Symbolic and Algebraic Computation},
Bonn, July 15-17, ACM Press, New York, 1991.

\bibitem{Coupling-II}
J.S. Kowalik and C.T. Kitzmiller, Editors,
{\em Coupling Symbolic and Numerical Computing in Expert Systems II},
North-Holland, New York, 1988.

\bibitem{Pavelle}
R. Pavelle, Editor,
{\em Applications of Computer Algebra},
proceedings of the 188th national meeting of the
American Chemical Society,
Kluwer, 1985, 74-93.

\bibitem{Bau}
H.H. Bau, T. Herbert, M.M. Yovanovich, Editors,
{\em Proceedings of Symbolic Computation in Fluid Mechanics and Heat Transfer},
HTD-Vol. 105, AMD-Vol. 97,
the Heat Transfer Division and the Applied Mechanics Division, ASME
ASME Winter Annual Meeting, Chicago, IL, Nov. 1988.

\bibitem{Noor}
A.K. Noor, I. Elishakoff, G. Hulbert, Editors,
{\em Symbolic Computations and Their Impact on Mechanics},
PCP-Vol. 205, The American Society of Mechanical Engineers,
New York, 1990.

\bibitem{Dubna}
{\em IV. International Conference on Computer Algebra in Physical
Research}, JINR, Dubna, 1990 (in press).

\bibitem{Houstis-Rice}
C.E. Houstis, J.R. Rice, and R.  Vichnevetsky,
{\em Expert Systems in Numerical Computing},
proceedings of the Second International Conference on
Expert Systems for Numerical Computing,
North-Holland, New York, 1991.
IMACS-ACM-SIGNUM, Purdue.

\bibitem{Saratoga}
B. Donald, D. Kapur and J. Mundy, Editors,
{\em Symbolic and Numerical Computation for Artificial Intelligence},
proceedings of the Saratoga Workshop on Integration of Numerical
and Symbolic Computing Methods, Saratoga Springs, 1990,
Academic Press, Cambridge, 1992, (in press).

\bibitem{Novosibirsk}
{\em CAAM-90, International Seminar on Computer Algebra and
Application to Mechanics}, Novosibirsk, Irkutsk, 1990 (in press).

\bibitem{IMACS91}
R. Vichnevetsky and J.J.H. Miller, Editors,
{\em IMACS'91 13th World Congress on Computation and Applied
Mathemetics}, Dublin, July 22-26,IMACS, Criterion Press, Dublin, 1991.

\bibitem{Beltzer}
A.I. Beltzer,
{\em Variational and Finite-Element Methods},
A Symbolic Computation Approach,
Springer-Verlag, Berlin, 1990.

\bibitem{Grossman}
R. Grossman, Editor,
{\em Symbolic Computation, Applications to Scientific Computing},
Frontiers in Applied Mathematics, SIAM, 1989.

\bibitem{Thinking}
Thinking Machines Corporation,
{\em Getting Started in CM Fortran},
Cambridge, MA, 1990.

\bibitem{Metcalf-Reid}
M. Metcalf and J. Reid,
{\em Fortran 90 Explanined},
Oxford Science Publications, Oxford, UK, 1990.

\bibitem{Knupp-Book}
P.M. Knupp and S. Steinberg,
{\em The Fundamentals of Grid Generation},
(approximately 150 page draft of a graduate level text,
contains extensive references to the literature).

\bibitem{Birkhoff-Lynch}
G. Birkhoff and R.E. Lynch,
{\em Numerical Solutions of Elliptic Problems},
SIAM Publications, Philadelphia, 1984.

\bibitem{Celia-gray}
M.A. Celia and W.G.Gray,
{\em Numerical Methods for Differential Equations},
Prentice Hall, Engelwood Cliffs, NJ, 1992.

\bibitem{Fletcher}
C.A.J. Fletcher,
{\em Computational Techniques for Fluid Dynamics},
Springer-Verlag, Berlin, 1988.

\bibitem{Forsythe}
G.E. Forsythe and W.R. Wasow,
{\em Finite Difference Methods for Partial Differential Equations},
Wiley, New York, 1960.

\cite{Golub-Ortega}
G.H. Golub and J.M. Ortega,
{\em Scientific Computing and Differential Equations},
Academic Press, Boston, 1991.

\bibitem{Hall}
C.A. Hall and T.A. Porsching,
{\em Numerical Analysis of Partial Differential Equations},
Prentice Hall, Englewood Cliffs, NJ, 1990.

\bibitem{Peyret-Taylor}
R. Peyret and T.D. Taylor,
{\em Computational Methods for Fluid Flow},
Springer-Verlag, New York, 1983.

\bibitem{Sodd}
G. Sodd,
xxx.

\bibitem{Strikwerda}
J.C. Strikwerda,
{\em Finite Difference Schemes and Partial Differential Equations},
Wadsworth \& Brooks\/Cole, Pacific Grove, 1989.

\bibitem{Wirth}
M.C. Wirth,
{\em On the Automation of Computational Physics},
Ph.D. Thesis, Davis School of Applied Science,
University of California, Lawrence Livermore Laboratory, 1980.

% Papers

\bibitem{Baras}
P. Baras, J. Blum, J.C. Paumier, P. Witomski, and R. Rechenmann,
{\em EVE: An object-centered knowledge-based PDE solver},
in \cite{Houstis-Rice}.

\bibitem{Bube-Strikwerda}
K.P. Bube and J.C. Strikwerda,
{\em Interior regularity estimates for
elliptic systems of difference equations},
SIAM J. Numer. Anal., {\bf 20} (1983), 653-670.

\bibitem{Cloutman}
L.D. Cloutman and L.W. Fullerton,
{\em Automated computation of modified equation},
Note, JCP, {\bf 29} (1978), 141-144.

\bibitem{Cook}
G.O. Cook, Jr.,
{\em ALPAL: A program to generate physics simulation codes
from natural descriptions}, Int. J. Mod. Phys. C, {\bf 1} (1990), 1-51.

\bibitem{Cook-Painter}
G.O. Cook, Jr. and J.F. Painter,
{\em ALPAL: A Tool to Generate Simulation Codes from Natural Descriptions},
in \cite{Houstis-Rice}.

\bibitem{Cook-Painter-Brown}
G.O. Cook, Jr., J.F. Painter, and S.A. Brown,
{\em How Symbolic Computation Boosts Productivity in the
Simulation of Partial Differential Equations},
to appear in the JCP.

\bibitem{Cook:91I}
G.O. Cook, Jr. and J.F. Painter,
{\em Construction of Large-Scale Simulation Codes Using ALPAL},
in \cite{IMACS91}.

\bibitem{Davenport}
J.H. Davenport,
{\em Computer Algebra for Cylindrical Algebraic Decomposition},
Bath Computer Science Technical Report 88-10.

\bibitem{Dewar}
M.C. Dewar,
{\em IRENA and integrated symbolic and numerical computation environment},
in \cite{ISSAC89}, 163-170.

\bibitem{Dewar:90}
M.C. Dewar and M.G. Richardson,
{\em Reconciling Symbolic and Numeric Computation in a Practical Setting},
in {\em Proceedings of DISCO'90}, Springer-Verlag, (1990), 195-204.

\bibitem{Flaherty}
J.E. Flaherty, M.  Benantar, R. Biswas, and P.K. More,
{\em Symbolic and parallel adaptive methods for partial differential equations},
in \cite{Saratoga}.

\bibitem{Frese-Sulsky}
M. Frese, D. Sulsky and S. Steinberg,
{\em Properties of the box scheme}, (in preparation).

\bibitem{Ganzha-Liska}
R. Liska and V. Ganzha,
{\em Application of the \protect{REDUCE} computer algebra system to
stability analysis of difference schemes},
in E. Kaltofen and S.M. Watt, editors, {\em Computers and
Mathematics '89}, 119-129, Springer-Verlag, New York, (1989).

\bibitem{Ganzha-Vorozhtsov}
V.G. Ganzha and E.V. Vorozhtsov,
{\em Stability analysis of difference initial-value problems with the aid
of \protect{REDUCE} system}, in \cite{Novosibirsk}.

\bibitem{Ganzha-Shashkov-Shapeev}
V. Ganzha, M.Yu. Shashkov, and V. Shapeev,
{\em Local approximation study of difference schemes by means of REDUCE},
in \cite{ISSAC90}.

\bibitem{Ganzha-Solovjev-Shashkov}
V. Ganzha, A.V. Solovjev, and M.Yu. Shashkov,
{\em Algorithms for operations with difference operators and grid functions
in symbolic form}, in \cite{Dubna}.

\bibitem{Ganza:85}
V.G. Ganzha, E.V. Vorozhtsov, S.I. Mazurik, and V.P. Shapeev,
{\em Symbolic manipulation on a computer and their application to
  generation and investigation of difference schemes},
in B.F. Caviness, editor, {\it EUROCAL '85 Vol. 2}, 335-347,
  Springer-Verlag, Berlin, (1985).

\bibitem{Ganza:87}
V.G. Ganzha and E.V. Vorozhtsov,
{\em The stability analysis of difference schemes by numerical solution of
  the generalized \protect{Routh-Hurwitz} problem},
Comp. Phys. Comm., {\bf 43}, 209-216, (1987).

\bibitem{Griewank}
A. Griewank,
{The chain rule revisited in scientific computing},
SIAM News, {\bf 24 },
Parts I, May 1991, 20-21, Part II, July 1991, 8-9, 24.

\bibitem{Griewank-Corliss}
A. Griewank and G.F. Corliss,
{\em Automatic Differentiation of Algorithms: Theory, Implementation and
Application}, SIAM, Philadelphia, 1991.

\bibitem{Harten}
L.P. Harten,
{\em Using MACSYMA to generate (somewhat) optimized FORTRAN code},
1984 MACSYMA Users' Conference, 1984, 524-544.

\bibitem{Hilfinger-Colella}
P.N. Hilfinger and P. Colella,
{\em FIDIL: A language for scientific programming},
in \cite{Grossman}, 97-138.

\bibitem{Hirayama}
H. Hirayama, M. Ikeda, and N. Sagawa,
{\em Solution Functions of PDEQSOL (Partial Differential EQuation
SOlver Language) for Fluid Problems}, in the Proceedings of Supercomputing '91,
Albuquerque, New Mexico, IEEE Computer Society Press, Los Alamitos, CA, 1991,
218-227.

\bibitem{Hulzen:83}
J.A. van Hulzen,
{\em Code optimization of multivariate polynomial schemes:
a pragmatic approach},
in J.A. van Hulzen, editor, {\it EUROCAL '83}, 
286-300, Springer-Verlag, Berlin, (1983).

\bibitem{Hulshof:84}
B.J.A. Hulshof and J.A. van Hulzen,
{\em Automatic Error Cumulation Control},
in J. Fitch, editor, {\it EUROSAM '84},  260-271, Springer-Verlag,
Berlin, (1984).

\bibitem{Hulshof:85}
B.J A. Hulshof and J.A. van Hulzen,
{\em An expression compression package for \protect{REDUCE} based on
  factorization and controlled expansion},
in B. S. Caviness, editor, {\it EUROCAL '85 Vol. 2}, 315-316,
Springer-Verlag, Berlin, (1985).

\bibitem{Heuvel:87}
P. van den Heuvel, J.A. van Hulzen, and V.V. Goldman,
{\em Automatic generation of \protect{FORTRAN}-coded jacobians and hessians},
in J. H. Davenport, editor, {\it EUROCAL '87}, Springer-Verlag, Berlin, (1989).

\bibitem{Hulzen-Hulshof-Gates}
J.A. van Hulzen, B.J.A. Hulshof, B.L. Gates, and M.C. van Heerwaarden,
{\em A code optimization package for REDUCE}, in \cite{ISSAC89}, 163-170.

\bibitem{Gates:86}
B. L. Gates,
{\em A numerical code generation facility for \protect{REDUCE}},
in B. W. Char, editor, {\it SYMSAC '86},  94-99, ACM, Waterloo, (1986).

\bibitem{Kant1}
E. Kant, F. Daube, W. MacGregor, and J. Wald,
{\em Automated synthesis of finite difference programs},
in \cite{Noor}.

\bibitem{Kant2}
E. Kant, F. Daube, W. MacGregor, and J. Wald,
{\em Scientific programming by automated synthesis},
Chapter 8 in Automating Software Design,
M. Lowry and R. McCartnery, Editors, AAAI Press, 1991.

\bibitem{Kant3}
E. Kant, F. Daube, W. MacGregor, and J. Wald,
{\em Knowledge-based program generation for mathematical modeling},
in \cite{Houstis-Rice}.

\bibitem{Kawabata-Kaneko}
S. Kawabata and T. Kaneko,
{\em A FORTRAN code optimizer for REDUCE output},
Technical Report, National Laboratory for High Energy Physics, Japan, 1987.

\bibitem{Leonard}
B.P. Leonard,
{\em The ULTIMATE conservative difference scheme
applied to unsteady one-dimensional advection},
Computer Methods in Applied Mechanics and Engineering, {\bf 88} (1991),
17-74.

\bibitem{Liska1}
R. Liska,
{\em Program for stability and accuracy analysis of finite difference methods},
Comp. Phys. Comm., {\bf 34} (1984), 175-186.

\bibitem{Liska2}
R. Liska,
{\em Automation of numerical solution of PDE systems},
in \cite{Dubna}.

\bibitem{Liska3}
R. Liska,
{\em Numerical code generation for finite difference schemes solving},
13th IMACS World Congress on Computation and Applied Mathematics,
Dublin, 1991 (in press).

\bibitem{Liska-Drska}
R. Liska and L. Drska,
{\em FIDE: A REDUCE package for automation of finite
difference method for solving PDE}, in \cite{ISSAC90}, 169-176.

\bibitem{Liska-Shashkov}
R. Liska and M.Yu. Shashkov,
{\em Algorithms for difference schemes construction on non-orthogonal
logically rectangular meshes}, in \cite{ISSAC91}, 419-426.

\bibitem{Mazurik-Vorozhtsov}
S. Mazurik and E. Vorozhtsov,
{\em Symbolic-numerical computation in the stability analysis
of difference schemes},  in \cite{ISSAC90}.

\bibitem{Drska-li-li:90B}
L. Drska, J. Limpouch and R. Liska,
{\em Simulation of laser-matter interaction in subpicosecond range using
  computer algebra for numerical code development},
in F. Smutn{\' y}, editor, {\it The Tenth Conference of
  Czechoslovack Physicists, Brno, August 27-31}, 113-116, Jednota {\v
  c}s. matematik{\accent'27 u} a fyzik{\accent'27 u}, Praha, (1990).

\bibitem{Drska-li-li:90T}
L. Drska, J. Limpouch and R. Liska,
{\em Simulation study of laser-matter interaction in subpicosecond range},
in N.L. Tsintsadze editor {\it 10-th European Summer School on Plasma Physics},
 Tbilisi, September 2-15,1990, World Scientific, Singapore,  (1991).

\bibitem{Drska-li-li:91}
L. Drska, J. Limpouch and R. Liska,
{\em Fokker-Planck simulations of laser-plasma
  interactions in plane and cylindrical geometries},
20-th ECLIM, European Conference on Laser Interaction with
  Matter, Warsaw, (1991).

\bibitem{Peskin}
R.L. Peskin,
{\em Symbolic computation in engineering user interface systems},
in \cite{Noor}

\bibitem{Rice}
J.R. Rice,
{\em Learning, teaching, optimization, and approximation},
in \cite{Houstis-Rice}.

\bibitem{Przekwas-Yang}
A.J. Przekwas and H.Q. Yang,
{\em Advanced CFD Methodology for Fast Transients Encountered in Nonlinear
Combustion Problems},
SBIR Phase I Final Report, 1989, CFD Research Corporation,
3313 Bob Wallace Avenue, Suite 205, Huntsville, AL, 35805.

\bibitem{Rosen}
B. Rosen,
{\em Automation of the derivation of dispersion relations: II},
JCP, {\bf 20}  (1976), 22-32.

\bibitem{Salari}
K. Salari, 
{\em The Influence of Sweep on Dynamic Stall Produced by
a Rapidly Pitching Wing},
Thesis, Mechanical Engineering, University of New Mexico, 1988.

\bibitem{Saunders}
B.D. Saunders, H.R. Lee, and S.K. Abdali,
{A Parallel Implementaion of the Cylindrical Algebraic Decomposition Algorithm},
in \cite{ISSAC89}.

\bibitem{Samarskii}
A.A. Samarskii, V.F. Tishkin, A.P. Favorskii, and M.Yu. Shashkov,
{\em Employment of the reference-Operator method in the construction
of finite difference analogs of tensor operations},
Diff. Eqns., {\bf 18} (1982), 881-885.

\bibitem{Thune:84}
M. Thun\'e,
{\em A software package for stability analysis of difference methods},
in B. Engquist and T. Smedsaas, editors, {\it PDE Software: Modules,
  Interfaces and Systems},  89-102, Elsevier Science Publishers, Amsterdam,
  (1984).

\bibitem{Serdjucova}
S.I. Serdjucova,
{\em Application of computer algebra in investigation of
difference schemes stability}, in \cite{Dubna}.

\bibitem{Wang:84}
P.S. Wang, T. Y.P. Chang, and J.A. van Hulzen,
{\em Code generation and optimization for finite element analysis},
in J. Fitch, editor, {\it EUROSAM '84},  237-247, Springer-Verlag,
  Berlin, (1984).

\bibitem{Wang:86}
P.S. Wang, H.Q. Tan, A.F. Saleeb, and T.Y.P. Chang,
{\em Code generation for hybrid mixed mode formulation in finite element
  analysis},
in B.W. Char, editor, {\it SYMSAC '86}, 45-52, ACM, Waterloo,
  (1986).

\bibitem{Wang:86a}
P.S. Wang,
{\em \protect{FINGER}: a symbolic system for automatic generation of
  numerical programs in finite element analysis},
J. Symb. Comp., 2, 305-316, (1986).

\bibitem{Sharma}
N. Sharma,
{\em Generating finite element programs for warp machine},
Proceedings of ASME Winter Annual Meeting, Chicago, IL, Nov. 1988.

\bibitem{Sharma-Wang-1}
N. Sharma and P.S. Wang,
{\em Symbolic derivation and automatic generation of parallel routines
for finite element analysis},
Lecture Notes in Computer Science, Gianni, P. (Ed.),
Proceedings International Symposium on Symbolic and Algebraic
Computations, Rome, Italy, July 4-8, 1988, 33-56.

\bibitem{Sharma-Wang-2}
N. Sharma and P.S. Wang,
{\em Generating parallel finite element programs for
shared-memory multiprocessors},
Department of Mathematics and Computer
Science, Kent State University, Kent, Feb. 1989.

\bibitem{Sharma-Wang-3}
N. Sharma and P.S. Wang,
{\em Generating finite element programs for shared memory multiprocessors},
in \cite{Noor}

\bibitem{Shu-Osher}
C.W. Shu and S. Osher,
{\em Efficient implementation of essentially non-oscillatory
shock-capturing schemes II },
J. Comput. Phy., {\bf 83} (1989), 32-78.

\bibitem{Toolkit}
S. Steinberg and P.J. Roache,
{\em A toolkit of symbolic manipulation programs
for variational grid generation}, in \cite{Coupling-II}, 103-116.

\bibitem{JCP}
S. Steinberg and P.J. Roache,
{\em Using MACSYMA to write FORTRAN subroutines},
J. of Symb. Comp., {\bf 2} (1986), 213-216.

\bibitem{Symbolic}
S. Steinberg and P.J. Roache,
{\em Grid generation: a variational and symbolic-computation approach},
Proceedings of the Numerical Grid Generation in Fluid Dynamics Conference,
J. H\"auser and C. Taylor (eds), Landshut, W. Germany, 1986.

\bibitem{Mechanics}
S. Steinberg and P.J. Roache,
{\em Using MACSYMA to write finite-volume based PDE solvers},
in \cite{Noor}

\bibitem{Steinberg-Roache-Bau}
S. Steinberg and P.J. Roache,
{\em Automatic generation of finite-difference code},
in \cite{Bau}.

\bibitem{Automatic}
S. Steinberg and P.J. Roache,
{\em Automatic generation of finite-volume and finite-difference code},
in \cite{Dubna}.

\bibitem{Basic}
S. Steinberg and P.J. Roache,
{\em Basic requirements for the automatic generation of FORTRAN code},
in \cite{Saratoga}.

\bibitem{Finite}
S. Steinberg and P.J. Roache,
{\em Finite-difference algorithm design and automatic code generation},
in \cite{Novosibirsk}.

\bibitem{Variational-Curve}
S. Steinberg and P.J. Roache,
{\em Variational curve and surface grid generation}.
Accepted for publication in JCP.

\bibitem{Symmetric-Operators}
S. Steinberg and P.J. Roache,
{\em Discretizing symmetric operators in general coordinates},
Preprint, Department of Mathematics and Statistics,
University of New Mexico, 1991, 110 pages.

\bibitem{Wade}
J.C. Strikwerda, B.A. Wade, and K.P. Bube,
{\em Regularity estimates up to the boundary
for elliptic systems of difference equations},
ICASE Report No. 86-31.

\bibitem{Vorozhtsov-Mazurik}
E. Vorozhtsov and S. Mazurik,
{\em Symbolic-numerical methods for the computer-aided stability investigation
of difference schemes}, in \cite{Dubna}.

\bibitem{Wang},
P.S. Wang,
{\em Advances in integrating symbolic, numeric and graphics computing},
in \cite{Dubna}.

\bibitem{Warming-Hyett}
R.F. Warming and B.J. Hyett,
{\em The modified equation approach to the stability and
accuracy analysis of finite-difference schemes},
JCP, {\bf 14} (1974), 159-179.

\bibitem{Weerawarana}
S. Weerawarana, E.N. Houstis, and J.R. Rice,
{\em An interactive symbolic-numeric interface to parallel ELLPACK for
building general PDE solvers}, preprint, Dept. of Computer Science,
Purdue University, 1990.

\bibitem{Wendroff}
B. Wendroff,
{\em The stability of the MacCormack's method for the scalar advection
equation}, Appl. Math. Lett., {\bf 4} (1991), 89-91.

\bibitem{Zippel}
R. Zippel,
{\em Symbolic/Numeric Techniques in Modelling and Simulation},
in \cite{Saratoga}.