Recent Publications
Books
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Miller J. J. H., O'Riordan E. and Shishkin G. I. (1996).
Fitted Numerical Methods for Singular Perturbation Problems.
World Scientific Publishing Co., Singapore, New Jersey, London, Hong
Kong, xiv + 166 pages.
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Zhuang F. G. (1995).
BAIL VII Proceedings.
International Academic Publishers, x + 332 pages.
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Miller J. J. H. (ed.) (1993).
Applications of Advanced Computational Methods for Boundary and
Interior Layers.
Boole Press, Dublin, vii + 213 pages.
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(1992).
BAIL VI Proceedings.
Boole Press, Dublin, 96 pages.
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Miller J. J. H. (ed.) (1991).
Computational Methods for Boundary and Interior Layers in Several
Dimensions.
Boole Press, Dublin, viii + 225 pages.
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Shishkin G. I. (1990).
Grid approximation of singularly perturbed elliptic and parabolic
equations.
Second Doctoral Thesis, Keldysh Institute of Applied Mathematics, USSR
Academy of Sciences, Moscow.
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Ben-ya G., Miller J. J. H. and Zhong-ci S. (eds.) (1988).
BAIL V Proceedings.
Boole Press, Dublin, ix + 442 pages.
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Godunov S. K., Miller J. J. H. and Novikov V. A. (eds.) (1986).
BAIL IV Proceedings.
Boole Press, Dublin, x + 443 pages.
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Miller J. J. H. (ed.) (1984).
BAIL III Proceedings.
Boole Press, Dublin, x + 339 pages.
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Miller J. J. H. (ed.) (1984).
BAIL III Short Course:
Advances in Computational Methods for
Boundary and Interior Layers.
Boole Press, Dublin, viii + 107 pages.
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Miller J. J. H. (ed.) (1982).
BAIL II Proceedings.
Boole Press, Dublin, x + 410 pages.
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Miller J. J. H. (ed.) (1982).
BAIL II Short Course: An Introduction to Computational and
Asymptotic Methods for Boundary and Interior Layers.
Boole Press, Dublin, viii + 107 pages.
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Miller J. J. H. (ed.) (1980).
BAIL I Proceedings.
Boole Press, Dublin, xii + 425 pages.
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Doolan E. P., Miller J. J. H. and Schilders W. H. A. (1980).
Uniform Numerical Methods for Problems with Initial and Boundary
Layers.
Irish edition, Boole Press, Dublin, xvi + 324 pages.
Russian language edition MIR, Moscow (1983).
Chinese language edition. Photocopied edition, Nanjing (1984).
Papers
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Miller J. J. H., Schilders W. H. A. and Wang S. (1999).
Application of finite element methods to the simulation of
semiconductor devices.
Rep. Progr. Phys., 62 (3), 277-353 .
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Farrell P. A., Hegarty A. F., Miller J. J. H., O'Riordan E. and Shishkin G. I. (1999).
On a fitted operator technique for singular perturbation
equations.
Finite Difference methods: Theory and Applications, Eds. A.A.
Samarskii, L. G. Vulkov, P. N. Vabishchevich, Nova Science Books, New
York.
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Shishkin G. I. (1999).
Grid approximations of singularly perturbed
equations with convective terms under small smoothness of the
derivatives involved in the equations.
Proceedings of
the International Workshop on Analytical and Computational Methods for
Convection-Dominated and Singularly Perturbed Problems, Lozenetz,
Bulgaria, August 27-31 1998, 12pp.
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Clavero C., Miller J. J. H., O'Riordan E. and Shishkin G. I. (1998).
An accurate numerical solution of a two dimensional heat transfer
problem with a parabolic boundary layer.
J. Comput. Math., 16 (1), 27-39.
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Farrell P. A., Miller J. J. H., O'Riordan E. and Shishkin G. I. (1998).
On the non-existence of e-uniform finite difference methods on
uniform meshes for semilinear two point boundary value problems.
Math. Comp., 67 (222), 603-617.
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Miller J. J. H., O'Riordan E. and Shishkin G. I. (1998).
Fitted numerical methods for four simple convection-diffusion
problems.
Procs. 2nd Asian Maths. Conf., Thailand 1995. Eds. S. Tangmanee & E.
Schultz, World Scientific Publishing Co., Singapore, New Jersey, Hong Kong, 444-448.
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Miller J. J. H., O'Riordan E., Shishkin G. I. and Shishkina L. P. (1998).
Fitted mesh methods for problems with parabolic boundary layers.
Math. Proc. Roy. Irish Acad., 98A (2), 173-190.
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Farrell P. A. and Shishkin G. I. (1998). On the convergence of iterative
methods for linear systems arising from singularly perturbed equations.
Proc. Copper Mountain Conf. on Iterative Methods, 1-7.
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Miller J. J. H., O'Riordan E. and Shishkin G. I. (1997).
Fitted mesh methods for the singularly perturbed reaction
diffusion problem.
Proc. Fifth International Colloquium on Numerical Analysis, Plovdiv,
Bulgaria August 1996, Ed. E. Minchev, Academic Publ., 99-105.
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Hegarty A. F., Miller J. J. H., O'Riordan E. and Shishkin G. I. (1997).
Numerical solution of elliptic convection-diffusion problems on fitted
meshes. CWI Quarterly, 10 (3,4), 239-251.
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Miller J. J. H. and O'Riordan E. (1997). The necessity of fitted
operators and Shishkin meshes for resolving thin layer phenomena.
CWI Quarterly, 10 (3,4), 207-213.
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Hemker P. W., Shishkin G. I. and Shishkina L. P. (1997).
The use of defect correction for the solution of parabolic singular
perturbation problems. Z. Angew. Math. Mech., 76 , 59-74.
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Shishkin G. I. (1997), Singularly perturbed boundary value problems with
concentrated sources and discontinuous initial conditions.
Comput. Math. Math. Phys., 37 (4), 417-434.
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Miller J. J. H., O'Riordan E. and Shishkin G. I. (1996).
On the use of fitted operator methods for singularly perturbed
partial differential equations.
Proceedings of International Conference on Advanced Mathematics,
Computations and Applications AMCA-95, Novosibirsk, June 20-24 1995
eds. A.S. Alekseev, N.S. Bakhvalov, 18pp.
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Farrell P. A., Miller J. J. H., O'Riordan E. and Shishkin G. I. (1996).
A uniformly convergent finite difference scheme for a singularly
perturbed semilinear equation. SIAM J. Numer. Anal. ,
33 (3),
1135-1149.
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Farrell P. A., Hemker P. W. and Shishkin G. I. (1996). Discrete
approximations for singularly perturbed boundary value problems with
parabolic layers III. J. Comput. Math., 14 (3), 273-290.
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Shishkin G. I. (1996). Approximation of solutions and of diffusion flows
in the case of singularly perturbed boundary value problems with
discontinuous initial conditions. Comput. Math. Math.
Phys.,
36, 1233-1250.
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Farrell P. A., Hemker P. W. and Shishkin G. I. (1996). Discrete
approximations for singularly perturbed boundary problems with parabolic
layers II. J. Comput. Math., 14 (2),
183-194.
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Hegarty A. F., Miller J. J. H., O'Riordan E. and Shishkin G. I. (1995).
Special meshes for finite difference approximations to an
advection-diffusion equation with parabolic layers.
J. Comput. Phys., 117, 47-54.
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Hegarty A. F., Miller J. J. H., O'Riordan E. and Shishkin G. I. (1995).
On a novel mesh for the regular boundary layers arising in
advection-dominated transport in two dimensions.
Comm. Numer. Methods Engrg.,
11, 435-441.
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Clavero C., Lisbona F. and Miller J. J. H. (1995).
Uniform convergence of arbitrary order on non-uniform meshes for a
singularly perturbed boundary value problem.
J. Comput. Appl. Math., 59, 155-171.
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Miller J. J. H., O'Riordan E. and Shishkin G. I. (1995).
On piecewise-uniform meshes for upwind and central difference
operators for solving singularly perturbed problems.
IMA J. Numer. Anal., 15, 89-99.
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Farrell P. A., Hegarty A. F., Miller J. J. H., O'Riordan E. and Shishkin G. I. (1995).
On the design of piecewise uniform meshes for solving
advection-dominated transport equations to a prescribed accuracy.
Notes Numer. Fluid Mech., Vieweg-Verlag, 49, 86-95.
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Hegarty A. F., Miller J. J. H., O'Riordan E. and Shishkin G. I. (1995).
Numerical results for advection-dominated heat transfer in a
moving fluid with a non-slip boundary condition.
Internat. J. Numer. Methods Heat Fluid Flow, 5 (2), 131-140.
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Hegarty A. F., Miller J. J. H., O'Riordan E. and Shishkin G. I. (1994).
Use of central difference operators for the solution of singularly
perturbed problems.
Comm. Numer. Methods Engrg., 10, 297-302.
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Hegarty A. F., Miller J. J. H., O'Riordan E. and Shishkin G. I. (1994).
Special numerical methods for convection-dominated laminar flows
at arbitrary Reynolds number.
East-West J. Numer. Math., 2, 65-74.
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Hegarty A. F., Miller J. J. H., O'Riordan E. and Shishkin G. I. (1994).
On numerical experiments with central difference operators on
special piecewise uniform meshes for problems with boundary layers.
Procs. 9th GAMM-Seminar Kiel, Jan 22-24 1993, 46 .
Notes Numer. Fluid Mech., Vieweg-Verlag, 167-176.
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Miller J. J. H., O'Riordan E., Petrenko E. A. and Shishkin G. I. (1993).
Special finite difference methods for calculating heat fields in
solid bodies with rapidly changing surface temperature.
Applications of Computational Methods for Boundary and Interior Layers,
ed. J.J.H. Miller, Boole Press, Dublin, 108-123.
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Hegarty A. F., Miller J. J. H., O'Riordan E. and Shishkin G. I. (1993).
Key to the computation of the transfer of a substance by
convection-diffusion in a laminar fluid.
Applications of Computational Methods for
Boundary and Interior Layers, ed. J.J.H. Miller, Boole Press, Dublin,
94-107.
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Hegarty A. F., Miller J. J. H., O'Riordan E. and Shishkin G. I. (1992).
Numerical results for a convection-diffusion problem with a
non-slip condition.
BAIL VI Procs. 6th International Conf on Boundary and Interior Layers.
Front Range Press, Colorado, 67-68.
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Miller J. J. H., Mullarkey E., O'Riordan E. and Shishkin G. I. (1991).
A simple recipe for uniformly convergent finite difference schemes
for singularly perturbed problems.
C. R. Acad. Sci. Paris, 312, Serie I, 643-648.
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Miller J. J. H. and Shishkin G. I. (1991).
On the construction of uniformly convergent finite difference
schemes for singularly perturbed problems for a quasilinear elliptic
equation.
Computational Methods for Boundary and Interior Layers in Several
Dimensions, ed. J.J.H. Miller, Boole Press, Dublin, 103-118.
Preprints
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Shishkin G. I..
Discrete Approximation of the Riemann Problem
for the Viscous Burgers Equation.
TCD Maths
department pre-print 99-12 .
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Farrell P. A., Hegarty A. F., Miller J. J. H., O'Riordan E. and
Shishkin G. I.. An iterative Re-uniform method for the numerical
solution of the Prandtl boundary-layer problem.
TCD Maths
department pre-print 99-11 .
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Farrell P. A., Hegarty A. F., Miller J. J. H., O'Riordan E. and
Shishkin G. I.. Numerical analysis of Re-uniform convergence for
boundary layer equations for a flat plate.
TCD Maths
department pre-print 99-08 .
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Farrell P. A., Hegarty A. F., Miller J. J. H., O'Riordan E. and
Shishkin G. I.. The e-uniform convergence of the discrete
derivatives for singularly perturbed problems.
TCD Maths
department pre-print 99-07.
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Farrell P. A., Hegarty A. F., Miller J. J. H., O'Riordan E. and
Shishkin G. I.. A technique for computing realistic values of the
error parameters for the numerical solutions of singular
perturbation problems.
TCD Maths
department pre-print 99-06.
High Performance Computing Reports
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O'Dea Enda, (September 1999).
Analysis of rounding errors in numerical solutions of a
singularly perturbed two-point boundary value problem with
Dirichlet and Neumann boundary conditions.
M. Sc. Thesis, Trinity College, Dublin.
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O'Reilly Gerard, (September 1998).
Numerical Study of Linear Convection Diffusion Problems in Two
Dimensions with Applications.
M. Sc. Thesis, Trinity College, Dublin.
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Musgrave Alison P., (September 1998).
Use of a supercomputer to analyse numerical methods for problems
with boundary layers.
M. Sc. Thesis, Trinity College, Dublin.
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