Number of communications to scientific meetings: 100+
Number of books: 4
Books
G.I. Shishkin. Grid Approximations of Singularly Perturbed
Elliptic and Parabolic Equations. Russian Acad. Sci., Ural Branch,
Ekaterinburg, 1992. 232 pp. (in Russian).
J.J.H. Miller, E. O'Riordan, G.I. Shishkin.
Fitted Numerical Methods for Singular Perturbation Problems.
Error Estimates in the Maximum Norm for Linear Problems in
One and Two Dimensions. World Scientific Publishing Co., Inc.,
Singapore, 1996. xiv + 166 pp. ISBN: 981-02-2462-1.
P.A. Farrell, A.F. Hegarty, J.J.H. Miller,
E. O'Riordan, G.I. Shishkin. Robust Computational Techniques
for Boundary Layers. Applied Mathematics, 16.
Chapman & Hall / CRC Press, Boca Raton, FL, 2000. xvi + 254 pp.
ISBN: 1-58488-192-5.
L.G. Vulkov, J.J.H. Miller, G.I. Shishkin (Eds.).
Analytical and Numerical Methods for Convection-Dominated and Singularly
Perturbed Problems. Nova Science Publishers, Inc., N.Y., 2000.
309 pp. ISBN: 1-56072-848-5.
G.I. Shishkin. A certain heat problem with a free boundary.
Dokl. Akad. Nauk SSSR, 1971, vol. 197, 1276-1279 (in Russian);
transl. in Soviet Math. Dokl., 1971, vol. 12, 682-686.
G.I. Shishkin. A certain problem of Stefan type with a
discontinuous movable boundary. Dokl. Akad. Nauk SSSR, 1975,
224 (6), 1276-1278 (in Russian).
G.I. Shishkin. The first boundary value problem for a
second order equation with small parameters multiplying the derivatives.
Differen. Uravnenija, 1977, 13 (2), 376-378 (in Russian).
G.I. Shishkin. A difference scheme for the solution of an elliptic
equation with a small parameter in a region with a curvilinear
boundary. Zh. Vychisl. Mat. Mat. Fiz., 1978, 18 (6), 1466-1475 (in Russian).
G.I. Shishkin. A difference scheme for the solution of elliptic
equations with small parameters multiplying the derivatives.
Mathematical models and numerical methods (Papers, Fifth Semester,
Stefan Banach Internat. Math. Center, Warsaw, 1975), pp. 89-92 (in Russian).
Banach Center Publ., 3, PWN, Warsaw, 1978.
G.I. Shishkin. The numerical solution of elliptic equations
with a small parameter multiplying the highest derivatives.
Dokl. Akad. Nauk SSSR, 1979, 245 (4), 804-808 (in Russian);
transl. in Soviet Math. Dokl., 1979, 20 (2), 368-371.
G.I. Shishkin. The grid method for solving elliptic
equations with discontinuous boundary conditions.
Zh. Vychisl. Mat. i Mat. Fiz., 1979, 19 (3), 640-651 (in Russian).
G.I. Shishkin. A difference scheme on a nonuniform grid
for differential equations with a small parameter multiplying the
highest-order derivative. Zh. Vychisl. Mat. Mat. Fiz., 1983, 23 (3),
609-619 (in Russian); transl. in
USSR Comput. Math. Math. Phys., 1983, 23 (3), 59-66.
G.I. Shishkin. Increasing the accuracy of solutions of
difference schemes for parabolic equations with a small parameter
multiplying the highest derivative. Zh. Vychisl. Mat. Mat. Fiz., 1984, 24 (6),
864-875 (in Russian).
G.I. Shishkin. A difference scheme for a fourth-order
differential equation with a small parameter multiplying the highest
derivative. Dokl. Akad. Nauk SSSR, 1984, 275 (6), 1323-1326 (in Russian);
transl. in Soviet Math. Dokl., 1984, 29 (2), 402-405.
G.I. Shishkin. A difference scheme for a fourth-order
ordinary differential equation with a small parameter multiplying
the highest derivative. Differen. Uravneniya, 1985, 21 (10), 1734-1742
(in Russian); transl. in Differential Equations, 1985, 21 (10),
1169-1176.
G.I. Shishkin. A difference scheme for a fourth-order elliptic
equation with a small parameter multiplying the highest derivatives.
Differen. Uravneniya, 1985, 21 (12), 2159-2165 (in Russian);
transl. in Differential Equations, 1985, 21 (12), 1465-1470.
G.I. Shishkin. Solution of a boundary value problem
for an elliptic equation with small parameter multiplying
the highest derivatives. Zh. Vychisl. Mat. i Mat. Fiz.,
1986, 26 (7), 1019-1031 (in Russian).
G.I. Shishkin. A difference scheme for an elliptic equation with
a small parameter at the highest derivatives. Dokl. Akad. Nauk SSSR,
1986, 286 (1), 57-61 (in Russian); transl. in Soviet Math. Dokl., 1986,
33 (1), 49-53.
G.I. Shishkin. Approximation of solutions of
singularly perturbed boundary value problems with a corner boundary layer.
Zh. Vychisl. Mat. i Mat. Fiz., 1987, 27 (9), 1360-1374 (in Russian).
G.I. Shishkin. Approximation of the solutions of singularly perturbed
boundary value problems with a corner boundary layer.
Dokl. Akad. Nauk SSSR, 1987, 296 (1), 39-43 (in Russian);
transl. in Soviet Math. Dokl., 1988, 36 (2), 240-244.
G.I. Shishkin. A difference scheme for a singularly perturbed equation
of parabolic type with a discontinuous initial condition.
Dokl. Akad. Nauk SSSR, 1988, 300 (5), 1066-1070 (in Russian); transl.
in Soviet Math. Dokl., 1988, 37 (3), 792-796.
G.I. Shishkin. Grid approximation of singularly perturbed parabolic
equations with internal layers. Sov. J. Numer. Anal. Math. Modelling, 1988,
3 (5), 392-407.
G.I. Shishkin. A difference scheme for a singularly perturbed
equation of parabolic type with a discontinuous boundary condition.
Zh. Vychisl. Mat. i Mat. Fiz., 1988, 28 (11), 1649-1662 (in Russian);
transl. in USSR Comput. Math. and Math. Phys., 1988, 28 (6), 32-41.
G.I. Shishkin. Approximation of solutions of
singularly perturbed boundary value problems
for an elliptic differential equation with parabolic boundary layers.
BAIL V (Shanghai, 1988), pp. 320-325, Boole Press Conf. Ser., 12,
Boole, Dun Laoghaire, 1988.
G.I. Shishkin. Approximation of solutions of singularly perturbed
boundary value problems with a parabolic boundary layer.
Zh. Vychisl. Mat. i Mat. Fiz., 1989, 29 (7), 963-977 (in Russian);
transl. in USSR Comput. Maths. Math. Phys., 1989, 29 (4), 1-10.
G.I. Shishkin. A difference scheme for a singularly perturbed equation
of parabolic type with discontinuous coefficients and concentrated factors.
Zh. Vychisl. Mat. i Mat. Fiz., 1989, 29 (9), 1277-1290 (in Russian);
transl. in USSR Comput. Maths. Math. Phys., 1989, 29 (5), 9-19.
G.I. Shishkin. Grid approximation of singularly perturbed elliptic
equations with discontinuous boundary conditions. Sov. J. Numer. Anal. Math.
Modelling, 1989, 4 (1), 69-85.
G.I. Shishkin. Grid approximation of singularly perturbed
boundary value problems with a regular boundary layer.
Sov. J. Numer. Anal. Math. Modelling, 1989, 4 (5), 397-417.
G.I. Shishkin. Grid approximation of singularly perturbed boundary
value problems with convective terms. Sov. J. Numer. Anal. Math. Modelling,
1990, 5 (2), 173-187.
G.I. Shishkin. Grid approximations of singularly perturbed
elliptic equations in domains with characteristic faces.
Soviet J. Numer. Anal. Math. Modelling, 1990, 5 (4-5), 327-343.
G.I. Shishkin. Grid approximation of singularly perturbed elliptic
equations in case of limit zero-order equations degenerating at the boundary.
Sov. J. Numer. Anal. Math. Modelling, 1990, 5 (6), 523-548.
G.I. Shishkin. Approximation of solutions of boundary value
problems with a parabolic boundary layer.
Numerical analysis and mathematical modelling, pp. 435-443 (in Russian).
Banach Center Publ., 24, PWN, Warsaw, 1990.
J. Miller, E. Mullarkey, E. O'Riordan, G. Shishkin. A simple recipe
for uniformly convergent finite-difference schemes for singularly perturbed
problems. C.R. Acad. Sci. Paris Ser. I Math., 1991, 312 (8), 643-648.
J.J.H. Miller, G.I. Shishkin. On the construction of uniformly
convergent finite difference schemes for singularly perturbed problems
for quasilinear elliptic equations. In: Computational Methods for
Boundary and Interior Layers in Several Dimensions, J.J.Miller ed.,
Boole Press, Dublin, 1991, 103-118.
G.I. Shishkin. Difference approximation of a singularly perturbed
quasilinear elliptic equation that degenerates into a first-order equation.
Dokl. Akad. Nauk SSSR, 1991, 317 (4), 845-849 (in Russian); transl. in
Soviet Math. Dokl., 1991, 43 (2), 562-566.
G.I. Shishkin. Grid approximation of singularly perturbed boundary
value problem for quasilinear elliptic equation degenerating into
first-order equation.
Sov. J. Numer. Anal. Math. Modelling, 1991, 6 (1), 61-81.
G.I. Shishkin. Grid approximation of singularly perturbed boundary
value problem for quasilinear parabolic equation in the case of complete
degeneracy in spatial variables. Sov. J. Numer. Anal. Math. Modelling,
1991, 6 (3), 243-261.
G.I. Shishkin. Grid approximation of certain singularly
perturbed problems of convective transfer with diffusion.
Sov. J. Numer. Anal. Math. Modelling, 1991, 6 (5), 395-420.
G.I. Shishkin. Difference approximation of singularly perturbed
parabolic equations that are degenerate on the boundary.
Zh. Vychisl. Mat. i Mat. Fiz., 1991, 31 (10), 1498-1511 (in Russian).
G.I. Shishkin. Grid approximation of a singularly perturbed
boundary value problem for a quasilinear elliptic equation in the case
of complete degeneration. Zh. Vychisl. Mat. i Mat. Fiz., 1991, 31 (12),
1808-1825 (in Russian).
G.I. Shishkin. Difference approximation of a singularly perturbed
boundary value problem for quasilinear elliptic equations degenerating into
a first-order equation. Zh. Vychisl. Mat. i Mat. Fiz., 1992, 32 (4),
550-566 (in Russian); transl. in USSR Comput. Maths. Math. Phys., 1992,
32 (4), 467-480.
G.I. Shishkin. A difference scheme for a singularly perturbed parabolic
equation degenerating on the boundary. Zh. Vychisl. Mat. i Mat. Fiz.,
1992, 32 (5), 717-732 (in Russian); transl. in USSR Comput. Maths. Math.
Phys., 1992, 32 (5), 621-636.
G.I. Shishkin. Grid approximation of singularly perturbed
boundary-value problems with sharply changing density of sources.
Rus. J. Numer. Anal. Math. Modelling, 1992, 7 (2), 145-167.
G.I. Shishkin. Methods of constructing grid approximations for
singularly perturbed boundary-value problems. Condensing-grid methods.
Russ. J. Numer. Anal. Math. Modelling, 1992, 7 (6), 537-562.
A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin.
Key to the computation of the transfer of a substance by
convection-diffusion in a laminar fluid. In: Applications of
Computational Methods for Boundary and Interior Layers,
J.J.H. Miller ed., Boole Press, Dublin, 1993, 94-107.
J.J.H. Miller, E. O'Riordan, E.A. Petrenko, G.I. Shishkin.
Special finite difference methods for calculating heat fields in
solid bodies with rapidly changing surface temperature. In:
Applications of Computational Methods for Boundary and Interior Layers,
J.J.H. Miller ed., Boole Press, Dublin, 1993, 108-123.
G.I. Shishkin. Grid approximation of a singularly perturbed
quasilinear equation in the presence of a transition layer.
Dokl. Akad. Nauk, 1993, 328 (3), 299-302 (in Russian);
transl. in Russian Acad. Sci. Dokl. Math., 1993, 47 (1), 83-88.
G.I. Shishkin. Grid approximation of the Dirichlet problem
for a singularly perturbed quasilinear parabolic equation in the presence
of a transition layer.
Dokl. Akad. Nauk, 1993, 332 (4), 424-427 (in Russian); transl. in
Russian Acad. Sci. Dokl. Math., 1994, 48 (2), 346-352.
G.I. Shishkin. Grid approximation of singularly perturbed degenerate
elliptic equations. Zh. Vychisl. Mat. i Mat. Fiz., 1993, 33 (4),
541-560 (in Russian); transl. in
Comput. Maths. Math. Phys., 1993, 33 (4), 493-509.
G.I. Shishkin. Grid approximation of singularly perturbed quasilinear
elliptic equations that degenerate into a zero-order equation.
Zh. Vychisl. Mat. i Mat. Fiz., 1993, 33 (9), 1305-1323 (in Russian);
transl. in Comp. Maths. Math. Phys., 1993, 33 (9), 1155-1170.
G.I. Shishkin. Iterative grid methods for singularly perturbed
elliptic equations degenerating into zero-order ones. Rus. J. Numer. Anal.
Math. Modelling, 1993, 8 (4), 341-369.
G.I. Shishkin. Method of splitting for singularly perturbed
parabolic equations. East-West J. Numer. Math., 1993, 1 (2), 147-163.
P.W. Hemker, G.I. Shishkin. Approximations of parabolic PDEs with a
discontinuous initial condition. East-West J. Numer. Math., 1993, 1 (4),
287-302.
A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin.
Special numerical methods for convection-dominated laminar flows at arbitrary
Reynolds number. East-West J. Numer. Math., 1994, 2 (1), 65-74.
A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin.
Use of central difference operators for the solution of singularly
perturbed problems. Comms. in Numer. Methods in Engineering,
1994, 10 (4), 297-302.
A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin.
On numerical experiments with central difference operators on special
piecewise uniform meshes for problems with boundary layers.
Notes on Numerical Fluid Mechanics, Vieweg-Verlag, 1994, vol. 46,
167-176.
P.W. Hemker, G.I. Shishkin. Discrete approximation of singularly
perturbed parabolic PDEs with a discontinuous initial condition.
Comp. Fluid Dynamics J., 1994, 2 (4). 375-392.
P.W. Hemker, G.I. Shishkin. On a class of singularly perturbed
boundary value problems for which an adaptive mesh technique is
necessary. In: Proceedings of the Second International Colloquium on
Numerical Analysis, Plovdiv, Bulgaria, August 13-17, 1993, eds
D.Bainov and V.Covachev. International Science Publishers, 1994, 83-92.
G.I. Shishkin. Difference approximation of the method of additive
separation of singularities for a singularly perturbed equation of parabolic
type. Zh. Vychisl. Mat. i Mat. Fiz., 1994, 34 (5), 720-738 (in Russian);
transl. in Comput. Maths. Math. Phys., 1994, 34 (5), 621-637.
G.I. Shishkin. Grid approximation of singularly perturbed quasilinear
elliptic and parabolic equations that degenerate into equations that
do not contain spatial derivatives.
Zh. Vychisl. Mat. i Mat. Fiz., 1994, 34 (11), 1632-1651 (in Russian);
transl. in Comput. Maths. Math. Phys., 1994, 34 (11), 1403-1419.
G.I. Shishkin. The method of additive separation of singularities for
quasilinear singularly perturbed elliptic and parabolic equations.
Zh. Vychisl. Mat. i Mat. Fiz., 1994, 34 (12), 1793-1814 (in Russian);
transl. in Comput. Maths. Math. Phys., 1994, 34 (12), 1541-1558.
G.I. Shishkin. Grid approximation of boundary value problem for singularly
perturbed quasilinear elliptic equations in the case of limit equations
that are degenerate on the boundary. Differen. Uravneniya,
1994, 30 (7), 1244-1258 (in Russian); transl. in
Differential Equations, 1994, 30 (7), 1152-1166.
G.I. Shishkin. Grid approximation of singularly perturbed equations
degenerating on the boundary. The case of coefficients changing
sharply in the neighborhood of a boundary layer. Mat. Model., 1994, 6 (5),
105-121 (in Russian).
P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin.
On the design of piecewise uniform meshes for solving advection-dominated
transport equations to a prescribed accuracy. Notes on Numerical Fluid
Mechanics, Vieweg-Verlag, 1995, 49, 86-95.
A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin.
Numerical results for advection-dominated heat transfer in a moving fluid
with a non-slip boundary condition. Intern. J. Numer. Meth. Heat & Fluid Flow,
1995, 5 (2), 131-140.
A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin.
Special meshes for finite difference approximations to an advection-diffusion
equation with parabolic layers. J. Comp. Phys., 1995, 117 (1), 47-54.
A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin.
On a novel mesh for the regular boundary layers arising in advection-dominated
transport in two dimensions. Comms. in Numer. Methods in Engineering,
1995, 11, 435-441.
J.J.H. Miller, E. O'Riordan, G.I. Shishkin. On piecewise-uniform meshes
for upwind and central difference operators for solving singularly perturbed
problems. IMA J. Numer. Anal., 1995, 15 (1), 89-99.
G.I. Shishkin. A difference scheme for the problem of the decay of
a discontinuity in the case of the viscous Burgers equation.
Dokl. Rus. Akad. Nauk, 1995, 342 (3), 313-317 (in Russian).
G.I. Shishkin. Grid approximation of singularly perturbed boundary
value problems for systems of elliptic and parabolic equations.
Zh. Vychisl. Mat. i Mat. Fiz., 1995, 35 (4), 542-564 (in Russian);
transl. in Comp. Maths. Math. Phys., 1995, 35 (4), 429-446.
G.I. Shishkin. Grid approximation of boundary value problems for
singularly perturbed quasilinear elliptic equations in the presence of
a transitional layer. Mat. Model., 1995, 7 (2), 72-88 (in Russian).
G.I. Shishkin. A problem for grid approximation of the diffusion flow
in numerical modelling of pollution transport. Mat. Model., 1995,
7 (7), 61-80 (in Russian).
G.I. Shishkin. Grid approximation of quasi-linear singularly
perturbed elliptic and parabolic equations with mixed boundary
conditions. Mat. Model., 1995, 7 (10), 111-126 (in Russian).
P.N. Vabishchevich, G.I. Shishkin. Difference schemes on locally
condensing grids. Differ. Uravn., 1995, 31 (7), 1179-1183
(in Russian); transl. in Differential Equations,
1995, 31 (7), 1121-1126.
J.J.H. Miller, E. O'Riordan, G.I. Shishkin. On the use of fitted
operator methods for singularly perturbed partial differential equations.
In: Advanced Mathematics, Computations and Applications,
Proceedings of the International Conference AMCA-95, Novosibirsk,
June 20-24, 1995, eds. A.S.Alekseev and N.S.Bakvalov. NCC Publisher,
Novosibirsk, 1995, 518-531.
G.I. Shishkin. Grid approximation of the solution and diffusion
flux for singularly perturbed parabolic equations. In: Proceedings of the
7-th International Conference on Boundary and Interior Layers:
Computational and Asymptotic Methods, Beijing, China, 1994.
International Academic Publishers, 1995, 12-19.
I.V. Pershin, G.I. Shishkin, I.V. Tselishcheva.
Parallelizing algorithms for the solution of boundary value problems
for singularly perturbed elliptic equations. In: Algorithms and
Programmed Tools of Parallel Computations. Ekaterinburg, Ural
Branch of Rus. Acad. Sci., 1995, 125-147 (in Russian).
P.A. Farrell, P.W. Hemker, G.I. Shishkin.
Discrete approximations for singularly perturbed boundary value problems
with parabolic layers, I. J. Comput. Maths., 1996, 14 (1), 71-97.
P.A. Farrell, P.W. Hemker, G.I. Shishkin.
Discrete approximations for singularly perturbed boundary value problems
with parabolic layers, II. J. Comput. Maths., 1996, 14 (2), 183-194.
P.A. Farrell, P.W. Hemker, G.I. Shishkin.
Discrete approximations for singularly perturbed boundary value problems
with parabolic layers, III. J. Comput. Maths., 1996, 14 (3), 273-290.
P.A. Farrell, J.J.H. Miller, E. O'Riordan, G.I. Shishkin. A uniformly
convergent finite difference scheme for a singularly perturbed semilinear
equation. SIAM J. Numer. Anal., 1996, 33 (3), 1135-1149.
G.I. Shishkin. Grid approximation of singularly perturbed equations
with convective terms in the case of mixed boundary conditions.
Differ. Uravn., 1996, 32 (5), 689-701 (in Russian); transl. in
Differential Equations, 1996, 32 (5), 698-711.
G.I. Shishkin. Locally one-dimensional difference schemes for
singularly perturbed parabolic equations.
Zh. Vychisl. Mat. i Mat. Fiz., 1996, 36 (2), 42-61 (in Russian);
transl. in Comp. Maths. Math. Phys., 1996, 36 (2), 165-180.
G.I. Shishkin. Grid approximation of parabolic equations with
singular initial conditions.
Zh. Vychisl. Mat. i Mat. Fiz., 1996, 36 (3), 73-92 (in Russian);
transl. in Comp. Maths. Math. Phys., 1996, 36 (3), 341-356.
G.I. Shishkin. Approximation of solutions and diffusion flows in
the case of singularly perturbed boundary value problems with discontinuous
initial conditions. Zh. Vychisl. Mat. i Mat. Fiz., 1996, 36 (9), 83-104
(in Russian); transl. in Comp. Maths. Math. Phys., 1996, 36 (9),
1233-1250.
G.I. Shishkin. The method of improving the accuracy of the approximate
solutions to singularly perturbed equations by defect correction. Rus. J. Numer.
Anal. Math. Model., 1996, 11 (6), 539-557.
G.I. Shishkin. Grid approximation of singularly perturbed
quasi-linear elliptic equations in the case of multiple solutions
of the reduced equation. Mat. Model., 1996, 8 (7), 109-127 (in Russian).
G.I. Shishkin, I.V. Tselishcheva. Parallel methods of solving
singularly perturbed boundary value problems for elliptic equations.
Mat. Model., 1996, 8 (3), 111-127 (in Russian, English summary).
G.I. Shishkin, P.N. Vabishchevich. Parallel domain decomposition methods
with the overlapping of subdomains for parabolic problems.
Math. Models and Methods in Applied Sciences, 1996, 6 (8), 1169-1185.
A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin.
Numerical solution of elliptic convection-diffusion problems on
fitted meshes. CWI Quarterly, 1997, 10 (3&4), 239-251.
P.W. Hemker, G.I. Shishkin, L.P. Shishkina.
The use of defect correction for the solution of parabolic singular
perturbation problems,
ZAMM - Z. angew. Math. Mech., 1997, 77 (1), 59-74.
V.L. Kolmogorov, G.I. Shishkin. Numerical methods for singularly
perturbed boundary value problems modelling diffusion processes. In:
Singular Perturbation Problems in Chemical Physics (J.J.H. Miller ed.),
Advances in Chemical Physics Series,
vol. XCVII, J.Wiley & Sons, 1997, 181-362.
G.I. Shishkin. Grid approximation of a singularly perturbed
Neumann problem for parabolic equations in the case of a discontinuous
boundary function. Zh. Vychisl. Mat. Mat. Fiz., 1997, 37 (3), 378-381
(in Russian); transl. in Comp. Math. Math. Phys., 1997, 37 (3), 370-373.
G.I. Shishkin. Singularly perturbed boundary value problems with
concentrated sources and discontinuous initial conditions.
Zh. Vychisl. Mat. Mat. Fiz., 1997, 37 (4), 429-446 (in Russian);
transl. in Comp. Math. Math. Phys., 1997, 37 (4), 417-434.
G.I. Shishkin. On finite difference fitted schemes for singularly
perturbed boundary value problems with a parabolic boundary layer.
J. Math. Anal. & Applications, 1997, 208, 181-204.
G.I. Shishkin. Acceleration of the process of the numerical solution
to singularly perturbed boundary value problems for parabolic equations
on the basis of parallel computations. Rus. J. Numer. Anal. Math. Model.,
1997, 12 (3), 271-291.
G.I. Shishkin, L.P. Shishkina, P.W. Hemker. A numerical
method with floating meshes for singularly perturbed problems
with a concentrated disturbance of the initial data. CWI Qurterly,
1997, 10 (3&4), 317-336.
G.I. Shishkin, I.V. Tselishcheva. The decomposition method
for singularly perturbed boundary value problems with local
perturbation of initial conditions. Equations with convective terms.
Izv. Vyssh. Uchebn. Zaved. Mat., 1997, No. 4, 98-107 (in Russian);
transl. in Russian Math. (Izv. VUZ), 1997, 41 (4), 96-105.
C. Clavero, J.C. Jorge, F. Lisbona, G.I. Shishkin. Splitting
time method and one dimensional special meshes for reaction-diffusiion
parabolic problems. In: Numerical Analysis and Its Applications,
First Intern. Workshop, WNAA'96, Rousse, Bulgaria, June 1996.
Proceedings (L.Vulkov, J.Wasniewski and P.Yalamov eds.) /
Lecture Notes in Computer Science, Springer-Verlag, 1997,
vol. 1196, 106-113.
V.L. Kolmogorov, G.I. Shishkin and L.P. Shishkina. Numerical analysis
in singularly perturbed boundary value problems modelling heat transfer
processes. In: Numerical Analysis and Its Applications, First
Intern. Workshop, WNAA'96, Rousse, Bulgaria, June 1996. Proceedings
(L.Vulkov, J.Wasniewski and P.Yalamov eds.) / Lecture Notes in
Computer Science, Springer-Verlag, 1997, vol. 1196, 250-257.
J.J.H. Miller, E. O'Riordan, G.I. Shishkin. Fitted mesh
methods for the singularly perturbed reaction diffusion problem. In:
Proceedings of the V-th International Colloquium on Numerical
Analysis, Plovdiv, Bulgaria, August 13-17, 1996, ed. E.Minchev.
Academic Publications, 1997, 99-105.
G.I. Shishkin. Grid approximations of the solution and diffusion flux
for singularly perturbed equations with Neumann boundary conditions. In:
Numerical Analysis and Its Applications,
First Intern. Workshop, WNAA'96,
Rousse, Bulgaria, June 1996. Proceedings, (L.Vulkov, J.Wasniewski and
P.Yalamov eds.) / Lecture Notes in Computer Science, Springer-Verlag,
1997, vol. 1196, 430-441.
G.I. Shishkin. Grid approximations for singularly perturbed
parabolic equations with discontinuous coefficients and concentrated
factors. Proc. of 9th Intern. Conference "Computational Modeling
and Computing in Physics" (Dubna, 1996).
Joint Inst. Nuclear Res., Dubna, 1997, 253-258.
C. Clavero, J.J.H. Miller, E.O'Riordan, G.I. Shishkin. An accurate
numerical solution of a two dimensional heat transfer problem with a
parabolic boundary layer. J. Comp. Math., 1998, 16 (1), 27-39.
C. Clavero, J.C. Jorge, F.Lisbona, G.I. Shishkin. A fractional step
method on a special mesh for the resolution of multidimensional evolutionary
convection-diffusion problems. Appl. Numer. Math., 1998, 27 (3), 211-232.
P.A. Farrell, J.J.H. Miller, E. O'Riordan, G.I. Shishkin.
On the non-existence of e-uniform finite difference methods
on uniform meshes for semilinear two-point boundary value problems.
Math. Comp., 1998, 67 (222), 603-617.
J.J.H. Miller, E. O'Riordan, G.I. Shishkin, L.P. Shishkina.
Fitted mesh methods for problems with parabolic boundary layers.
Mathematical Proceedings of the Royal Irish Academy, 1998,
98A (2), 173-190.
G.I. Shishkin. Grid approximations of singularly perturbed systems
of parabolic convection-diffusion equations with counterflow.
Siberian J. Numer. Math., 1998, 1 (3), 281-297.
G.I. Shishkin. A grid approximation for the Riemann problem in
the case of the Burgers equation.
Zh. Vychisl. Mat. Mat. Fiz., 1998, 38 (8), 1418-1420 (in Russian);
transl. in Comp. Math. Math. Phys., 1998, 38 (8),
1361-1363.
G.I. Shishkin. Approximation of singularly perturbed elliptic
equations with convective terms in the case of a flow impinging on an
impermeable wall. Zh. Vychisl. Mat. Mat. Fiz., 1998, 38 (11), 1844-1859
(in Russian); transl. in Comp. Math. Math. Phys., 1998, 38 (11),
1768-1782.
G.I. Shishkin. Finite-difference approximations of singularly
perturbed elliptic equations.
Zh. Vychisl. Mat. Mat. Fiz., 1998, 38 (12), 1989-2001 (in Russian);
transl. in Comp. Math. Math. Phys., 1998, 38 (12), 1909-1921.
G.I. Shishkin. Grid approximation of singularly perturbed
systems of elliptic and parabolic equations with convective terms.
Differen. Uravneniya, 1998, 34 (12), 1686-1696 (in Russian);
transl. in Differential Equations, 1998, 34 (12), 1693-1704.
G.I. Shishkin. A posteriori piecewise uniform grids
for singularly perturbed elliptic equations of a
reaction-diffusion type. Rus. J. Numer. Anal. Math. Modelling,
1998, 13 (5), 411-423.
G.I. Shishkin. Grid approximations of parabolic equations with
a small parameter multiplying the space and time derivatives.
Reaction-diffusion equations. Mathematica Balkanica.
New Series, 1998, 12 (1&2), 179-214.
P.A. Farrell, G.I. Shishkin. On the convergence
of iterative methods for linear systems arising from singularly
perturbed equations. Proc. of Copper Mountain Conf. on Iterative
Methods, 1998, 1-7.
P.W. Hemker, G.I. Shishkin, L.P. Shishkina.
A defect correction method for parabolic singular perturbation
problems on a rectangle. Proceedings of the Second International
Conference "Finite-Difference Methods: Theory and Application",
Minsk, 1998. V. 2. P. 30-34.
J.J.H. Miller, E. O'Riordan and G.I. Shishkin.
Fitted numerical methods for four simple convection-diffusion problems.
Proceedings of the Second Asian Mathematical Conference
on Numerical Analysis, Thailand 1995 (Nakhon Ratchasima),
S. Tangmanee and E. Schulz eds., World Sci. Publishing, River Edge, NJ,
1998. P. 444-448.
G.I. Shishkin. A decomposition method for singularly
perturbed reaction-diffusion equations with discontinuous boundary
conditions. Proceedings of the Second International Conference
"Finite-Difference Methods: Theory and Application", Minsk, 1998.
V. 3. P. 77-84.
G.I. Shishkin. Singularly perturbed boundary value problems
with locally perturbed initial conditions. Equations with convective
terms. Zh. Vychisl. Mat. Mat. Fiz., 1999, 39 (2), 262-279 (in Russian);
transl. in Comp. Math. Math. Phys., 1999, 39 (2), 249-265.
G.I. Shishkin. Increasing the accuracy of approximate
solutions by residual correction for singularly perturbed equations
with convective terms. Izv. Vyssh. Uchebn. Zaved. Mat., 1999,
No. 5, 81-93 (in Russian); transl. in Russian Math. (Iz. VUZ),
1999, 43 (5), 77-89.
G.I. Shishkin. Optimization of piecewise-uniform grids
for singularly perturbed equations of reaction-diffusion
type. Differen. Uravneniya, 1999, 35 (7), 990-997 (in Russian);
transl. in Differential Equations, 1999, 35 (7), 1000-1007.
G.I. Shishkin. Grid approximation of singularly perturbed
boundary value problems in a nonconvex domain with a piecewise
smooth boundary. Mat. Model., 1999, 11 (11), 75-90 (in Russian).
G.I. Shishkin. Grid approximation of singularly perturbed
boundary value problems on locally refined meshes. Reaction-diffusion
equations. Mat. Model., 1999, 11 (12), 87-104 (in Russian).
G.I. Shishkin. Locally one-dimensional difference schemes for
singularly perturbed parabolic equations with convective terms.
Rus. J. Numer. Anal. Math. Modelling, 1999, 14 (6), 495-511.
P.A. Farrell, A. Hegarty, J.J.H. Miller, E. O'Riordan,
G.I. Shishkin. On a fitted operator technique for singular
perturbation equations. In: Finite Difference Methods: Theory
and Applications (A.A. Samarskii, L.G. Vulkov and P.N. Vabishchevich
eds.), [Proceedings of the International Conference,
Rousse, Bulgaria, August 10-13, 1997], Nova Science, N.Y., 1999, 71-78.
P.W. Hemker, G.I. Shishkin, L.P. Shishkina.
The numerical solution
of a Neumann problem for parabolic singular perturbed equations
with high-order time accuracy. In: Recent Advances in Numerical
Methods and Applications II (O.P. Iliev, M.S. Kaschiev, S.D.
Margenov, B.H. Sendov and P.S. Vassilevski eds.),
Proceedings of the Fourth International Conference, Sofia, Bulgaria,
August 19-23, 1998, World Scientific, Singapore, 1999, 27-39.
P.W. Hemker, G.I. Shishkin, L.P. Shishkina.
An e-uniform defect-correction method for a
parabolic convection-diffusion problem. In: Recent Advances
in Numerical Methods and Applications II (O.P. Iliev, M.S. Kaschiev,
S.D. Margenov, B.H. Sendov and P.S. Vassilevski eds.),
Proceedings of the Fourth International Conference, Sofia, Bulgaria,
August 19-23, 1998, World Scientific, Singapore, 1999, 521-529.
G.I. Shishkin. Grid approximation of singularly perturbed
parabolic equations with convective terms in the case of impermeable
walls. In: Finite Difference Methods: Theory and Applications
(A.A. Samarskii, L.G. Vulkov and P.N. Vabishchevich eds.),
[Proceedings of the International Conference, Rousse, Bulgaria,
August 10-13, 1997], Nova Science, N.Y., 1999, 229-239.
G.I. Shishkin. Grid approximation of singularly perturbed
elliptic equations with convective terms in unbounded domains.
In: Recent Advances in Numerical Methods and Applications II
(O.P. Iliev, M.S. Kaschiev, S.D. Margenov, B.H. Sendov and
P.S. Vassilevski eds.), Proceedings of the Fourth International
Conference, Sofia, Bulgaria, August 19-23, 1998, World Scientific,
Singapore, 1999, 547-555.
G.I. Shishkin, I.V. Tselishcheva. Approximations of the
solution and diffusion fluxes for singularly perturbed parabolic
equations with convective terms on a rectangle. In: Finite Difference
Methods: Theory and Applications (A.A. Samarskii, L.G. Vulkov and
P.N. Vabishchevich eds.), [Proceedings of the International Conference,
Rousse, Bulgaria, August 10-13, 1997], Nova Science, N.Y., 1999, 241-249.
I.V. Tselishcheva, G.I. Shishkin. A decomposition method for
singularly perturbed reaction-diffusion equations. In: Recent
Advances in Numerical Methods and Applications II (O.P. Iliev, M.S.
Kaschiev, S.D. Margenov, B.H. Sendov and P.S. Vassilevski eds.),
Proceedings of the Fourth International Conference, Sofia, Bulgaria,
August 19-23, 1998, World Scientific, Singapore, 1999, 556-564.
P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan E.,
G.I. Shishkin.
The e-uniform convergence of the discrete
derivatives for singularly perturbed problems.
TCDMATH Report Series, the School of Mathematics,
Trinity College, Dublin.
Preprint TCDMATH 99-07 (1999).
P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan E.,
G.I. Shishkin.
Numerical analysis of Re-uniform convergence for
boundary layer equations for a flat plate.
TCDMATH Report Series, the School of Mathematics,
Trinity College, Dublin.
Preprint TCDMATH 99-08 (1999).
P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan E.,
G.I. Shishkin.
An iterative Re-uniform method for the numerical solution
of the Prandtl boundary-layer problem.
TCDMATH Report Series, the School of Mathematics,
Trinity College, Dublin.
Preprint TCDMATH 99-11 (1999).
G.I. Shishkin. Discrete approximation of the Riemann problem
for the viscous Burgers equation.
TCDMATH Report Series, School of Mathematics,
Trinity College, Dublin.
Preprint TCDMATH 99-12 (1999).
J. Etienne, J.J.H. Miller, G.I. Shishkin.
A robust layer-resolving numerical method for a free convection
problem. TCDMATH Report Series, the School of
Mathematics, Trinity College, Dublin.
Preprint TCDMATH 00-03 (2000).
B. Gahan, J.J.H. Miller, G.I. Shishkin.
Accurate numerical method for Blasius' problem
for flow past a flat plate with mass transfer.
TCDMATH Report Series, the School of
Mathematics, Trinity College, Dublin.
Preprint TCDMATH 00-05 (2000).
P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan E.,
G.I. Shishkin.
An experimental technique for computing parameter-uniform
error estimates for numerical solutions of singular perturbation
problems, with an application to Prandtl's problem
at high Reynolds number.
TCDMATH Report Series, the School of
Mathematics, Trinity College, Dublin.
Preprint TCDMATH 00-06 (2000).
B. Gahan, J.J.H. Miller, G.I. Shishkin.
Reynolds-uniform numerical method for Prandtl's problem
with suction-blowing based on Blasius' approach.
TCDMATH Report Series, the School of
Mathematics, Trinity College, Dublin.
Preprint TCDMATH 00-07 (2000).
S. Matthews, J.J.H. Miller, E. O'Riordan, G.I. Shishkin.
A parameter robust numerical method for a system of singularly
perturbed ordinary differential equations.
DCU Maths. Dept. Preprint Series, Dublin City University.
Preprint MS-00-03 (2000).
S. Matthews, E. O'Riordan, G.I. Shishkin.
Numerical methods for a system of singularly perturbed
reaction-diffusion equations.
DCU Maths. Dept. Preprint Series, Dublin City University.
Preprint MS-00-06 (2000).
P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan,
G.I. Shishkin. Parameter-uniform numerical methods for a class of
singularly perturbed problems with a Neumann boundary condition.
DCU Maths. Dept. Preprint Series, Dublin City University.
Preprint MS-00-11 (2000).
P.W. Hemker, G.I. Shishkin, L.P. Shishkina.
High-order time-accurate schemes for parabolic
singular perturbation problems with convection.
CWI Research Reports. Modelling, Analysis
and Simulation (MAS) Report Series.
Preprint MAS-R0101 (2001).
P.A. Farrell, J.J.H. Miller, E. O'Riordan,
G.I. Shishkin. Parameter-uniform fitted mesh method
for quasilinear differential equations with boundary layers.
DCU Maths. Dept. Preprint Series,
Dublin City University.
Preprint MS-01-01 (2001).
H. MacMullen, E. O'Riordan, G.I. Shishkin.
The convergence of classical Schwarz methods applied to
convection-diffusion problems with regular boundary layers.
DCU Maths. Dept. Preprint Series,
Dublin City University.
Preprint MS-01-02 (2001).
P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan,
G.I. Shishkin. Global maximum norm parameter-uniform numerical
method for a singularly perturbed convection-diffusion problem
with discontinuous convection coefficient.
DCU Maths. Dept. Preprint Series,
Dublin City University.
Preprint MS-01-06 (2001).
P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan,
G.I. Shishkin. Singularly perturbed convection diffusion problems
with boundary and weak interior layers.
DCU Maths. Dept. Preprint Series,
Dublin City University.
Preprint MS-01-07 (2001).
R.K. Dunne, E. O'Riordan, G.I. Shishkin.
A fitted mesh method for a class of singularly perturbed parabolic problems
with a boundary turning point.
DCU Maths. Dept. Preprint Series,
Dublin City University.
Preprint MS-01-10 (2001).
G.I Shishkin. Approximations of solutions and derivatives for
singularly perturbed elliptic convection-diffusion equations.
TCDMATH Report Series, the School of
Mathematics, Trinity College, Dublin.
Preprint TCDMATH 01-16 (2001).
P.W. Hemker, G.I. Shishkin, L.P. Shishkina.
High-order time-accurate schemes for singularly perturbed parabolic
convection-diffusion problems with Robin boundary conditions.
CWI Research Reports. Modelling, Analysis
and Simulation (MAS) Report Series.
Preprint MAS-R0207 (2002).
P.W. Hemker, G.I. Shishkin, L.P. Shishkina.
High-Order accurate decomposition methods based on Richardson's extrapolation
for a singularly perturbed elliptic reaction-diffusion equation on a strip.
TCDMATH Report Series, the School of
Mathematics, Trinity College, Dublin.
Preprint TCDMATH 02-04 (2002).
J.J.H. Miller, G.I. Shishkin, L.P. Shishkina, B. Koren.
Grid approximation of a singularly perturbed boundary value problem modelling
heat transfer in the case of flow over a flat plate with suction of the
boundary layer. TCDMATH Report Series, the School of
Mathematics, Trinity College, Dublin.
Preprint TCDMATH 02-01 (2002).
G.I. Shishkin. Limitations of adaptive mesh refinement methods
for a singularly perturbed parabolic equation in a composed domain with a
concentrated source on the moving interface boundary.
TCDMATH Report Series, the School of
Mathematics, Trinity College, Dublin.
Preprint TCDMATH 02-02 (2002).
J.J.H. Miller, R.E. O'Malley, G.I. Shishkin.
Grid approximation of multiscale problems arising in singularly perturbed
parabolic reaction-diffusion equations in an unbounded domain.
TCDMATH Report Series, the School of
Mathematics, Trinity College, Dublin.
Preprint TCDMATH 02-05 (2002).
G.I. Shishkin. On conditioning of a Schwarz method for singularly
perturbed convection--diffusion equations in the case of
disturbances in the data of the boundary value problem.
TCDMATH Report Series, the School of Mathematics,
Trinity College Dublin.
Preprint TCDMATH 03-01 (2003).
G.I. Shishkin. Improved e-uniform accurate
schemes for singularly perturbed elliptic convection-diffusion 3D problems.
The Richardson extrapolation technique. TCDMATH Report Series,
the School of Mathematics, Trinity College Dublin. Preprint TCDMATH 03-08 (2003).
P.W. Hemker, G.I. Shishkin, and L.P. Shishkina.
Domain decomposition method for a singularly perturbed quasilinear
parabolic convection-diffusion equation.
TCDMATH Report Series, the School of Mathematics,
Trinity College Dublin.
Preprint TCDMATH 03-02 (2003).
P.W. Hemker, G.I. Shishkin, L.P. Shishkina. Improved
e-uniform accurate schemes for singularly
perturbed parabolic convection-diffusion problems. Defect-correction
technique. TCDMATH Report Series, the School of Mathematics, Trinity College Dublin.
Preprint TCDMATH 03-07 (2003).
P.A. Farrell, A.F. Hegarty, J.J.H. Miller, E. O'Riordan, G.I. Shishkin.
Numerical techniques for flow problems with singularities.
TCDMATH Report Series, the School of Mathematics,
Trinity College Dublin.
Preprint TCDMATH 03-03 (2003).
J.S. Butler, J.J.H Miller, G.I. Shishkin.
A Reynolds-uniform numerical method for Prandtl's boundary layer problem
for flow past a wedge. TCDMATH Report Series, the School of Mathematics, Trinity College
Dublin.
Preprint TCDMATH 03-05 (2003).
J.S. Butler, J.J.H Miller, G.I. Shishkin.
A Reynolds-uniform numerical method for Prandtl's boundary layer problem
for flow past a plate with mass transfer.
TCDMATH Report Series, the School of Mathematics, Trinity College
Dublin.
Preprint TCDMATH 03-06 (2003).
A.R. Ansari, J.J.H. Miller, G.I. Shishkin.
Robust numerical method for periodic driven flow through a pipe.
ULMS Report Series, Department of Mathematics & Statistics, University of
Limerick, Ireland. Preprint ULMS-03-01 (2003).
P.A. Farrell, E. O'Riordan, G.I. Shishkin. A class of singularly perturbed
semilinear differential equations with interior layers. Mathematical Sciences
Preprint Series, Dublin City University. Preprint MS-03-08 (2003).