Mathematics

Research Interests:

Singularly perturbed differential equations. Numerical analysis. Shishkin meshes.

Selected Peer Reviewed Journals

• Gracia, J.L. and O'Riordan, E. 2012. A singularly perturbed parabolic problem with a layer in the initial condition. Applied Mathematics And Computation, 219, 2, pp498-510.
• Eugene O'Riordan. 2012. Opposing flows in a one dimensional convection-diffusion problem. Central European Journal Of Mathematics, 10, 1, pp85-100.
• Eugene O'Riordan and J. Quinn. 2012. A Singularly Perturbed Convection Diffusion Turning Point Problem with an Interior Layer. Computational Methods In Applied Mathematics, 12, 2, pp206-220.
• J.L. Gracia and Eugene O'Riordan. 2012. A singularly perturbed convection diffusion problem with a moving interior layer. International Journal Of Numerical Analysis And Modeling, 9, 4, pp823-843.
• E. O¿ Riordan and J. Quinn. 2012. Parameter¿uniform numerical methods for some singularly perturbed nonlinear initial value problems. Numerical Algorithms, 61, 4, pp579-611.
• Eugene O'Riordan and Jason Quinn. 2011. Parameter-uniform numerical methods for some Linear and Nonlinear Singularly Perturbed Convection Diffusion Boundary Turning Point Problems. Bit Numerical Mathematics, 51,, pp317-337.
• Eugene O'Riordan and Jason Quinn. 2011. Nonlinear Singularly Perturbed Interior Layer Problem. Lecture Notes In Computational Science And Engineering, 81,, pp187-195.
• Gracia, Jose-Luis and O'Riordan, Eugene. 2011. A singularly perturbed convection diffusion parabolic problem with an interior layer. Lecture Notes In Computational Science And Engineering, 81,, pp139-146.
• O'Riordan, Eugene and de Falco, Carlo. 2011. A parameter robust Petrov-Galerkin scheme for advection-diffusion-reaction equations. Numerical Algorithms, 56, 1, pp107-127.
• O'Riordan, Eugene and Pickett, Maria. 2011. A parameter--uniform numerical method for a singularly perturbed two parameter elliptic problem. Advances In Computational Mathematics, 35, , pp57-82.
• de Falco, Carlo and O'Riordan,Eugene. 2010. Interior layers in a reaction--diffusion equation with a discontinuous diffusion coefficient. International Journal Of Numerical Analysis And Modeling, 7, 3, pp444-461.
• J. L. Gracia, F. J. Lisbona and Eugene O'Riordan. 2010. A coupled system of singularly perturbed parabolic reaction-diffusion equations. Advances In Computational Mathematics, 32, , pp43-62.
• Kopteva, N and Eugene O'Riordan. 2010. Shishkin meshes in the numerical solution of singularly perturbed differential equations. International Journal Of Numerical Analysis And Modeling, 7, 3, pp393-415.
• de Falco, C and Eugene O'Riordan. 2009. A patched mesh method for singularly perturbed reaction-diffusion equations. Lecture Notes In Computational Science And Engineering, 69, , pp117-128.
• de Falco, C. and Eugene O'Riordan. 2009. Singularly perturbed reaction-diffusion problem with a boundary turning point. Lecture Notes In Computational Science And Engineering, 69,, pp129-140.
• E. O' Riordan and M. Stynes,. 2009. Numerical analysis of a strongly coupled system of two singularly perturbed convection-diffusion problems. Advances In Computational Mathematics, 30, , pp101-121.
• Farrell,P and Eugene O'Riordan. 2009. Examination of the performance of robust numerical methods for singularly perturbed quasilinear problems with interior layers. Lecture Notes In Computational Science And Engineering, 69,, pp129-140.
• Gracia; J. L. , Lisbona F. J. , Madaune-Tort, M. and O'Riordan, E. 2009. A system of singularly perturbed semilinear equations. Lecture Notes In Computational Science And Engineering,, pp163-172.
• O'Riordan, Eugene; Stynes, J. and Stynes. M. 2009. An iterative numerical algorithm for a strongly coupled system of singularly perturbed convection-diffusion problems. Lecture Notes In Computer Science, 5434,, pp104-115.
• P. A. Farrell, E. O' Riordan and G. I. Shishkin. 2009. A class of singularly perturbed quasilinear differential equations with interior layers. Mathematics Of Computation, 78, 265, pp103-127.
• R. K. Dunne, E. O' Riordan and G. I. Shishkin. 2009. Fitted mesh numerical methods for singularly perturbed elliptic problems with mixed derivatives. Ima Journal Of Numerical Analysis (oxford University Pr, 29, , pp712-730.
• E. O' Riordan, J. Stynes and M. Stynes. 2008. A parameter-uniform finite difference method for a coupled system of convection-diffusion two-point boundary value problems. Numerical Mathematics: Theory, Methods And Applications, 1, 2, pp176-197.
• Eugene O'Riordan and G. I. Shishkin. 2008. Parameter uniform numerical methods for singularly perturbed elliptic problems with parabolic boundary layers. Applied Numerical Mathematics (elsevier), 58, , pp1761-1772.
• E. O'Riordan and G. I. Shishkin,. 2007. A technique to prove parameter--uniform convergence for a singularly perturbed convection diffusion equation. Journal Of Computational And Applied Mathematics, 206, , pp136-145.
• R. K. Dunne, E. O' Riordan and M. M. Turner. 2007. A numerical method for a singular perturbation problem arising in the modelling of plasma sheaths. International Journal Of Computing Science And Mathematics, 1, 2/3/4, pp322-342.
• E. O'Riordan, M.L. Pickett and G.I. Shishkin. 2006. Parameter-uniform finite difference schemes for singularly perturbed parabolic diffusion-convection-reaction problems,. Mathematics Of Computation, 75, , pp1135-1154.
• E. O'Riordan, M.L. Pickett and G.I. Shishkin,. 2006. Numerical methods for singularly perturbed elliptic problems containing two perturbation parameters. Mathematical Modelling And Analysis, 11, 2, pp199-212.
• J.L. Gracia, E.O¿Riordan and M.L. Pickett,. 2006. A parameter robust second order numerical method for a singularly perturbed two--parameter problem. Applied Numerical Mathematics (elsevier), 56, , pp962-980.
• J.L. Gracia, E.O¿Riordan,. 2006. A defect-correction parameter-uniform numerical method for a singularly perturbed convection-diffusion problem in one dimension. Numerical Algorithms, 41, 4, pp359-385.
• C. Clavero, J.L. Gracia and E.O¿Riordan,. 2005. A parameter robust numerical method for a two dimensional reaction-diffusion problem. Mathematics Of Computation, 74, , pp1743-1758.
• M. J. O Reilly and E. O¿Riordan. 2005. A Shishkin mesh for a singularly perturbed Riccati equation. Journal Of Computational And Applied Mathematics, 182, 2, pp372-387.
• P. A. Farrell, E. O' Riordan and G. I. Shishkin,. 2005. A class of singularly perturbed semilinear differential equations with interior layers. Mathematics Of Computation, 74, , pp1759-1776.
• P. A. Farrell, A. F. Hegarty, J.J.H. Miller, E. O' Riordan and G. I. Shishkin,. 2004. Global maximum norm parameter¿uniform numerical method for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient. Mathematical And Computer Modelling, 40, , pp1375-1392.
• A. D. Wood, E. O¿Riordan, N. Sweeney and R. B. Paris,. 2004. Marginal states of the resistive tearing mode with flow in cylindrical geometry,. Journal Of Plasma Physics, 70, 2, pp155-161.
• E. O' Riordan and G. I. Shishkin. 2004. Singularly perturbed parabolic problems with non-smooth data. Journal Of Computational And Applied Mathematics, 166, 1, pp233-245.
• P. A. Farrell, A. F. Hegarty, J. J. H. Miller, E. O' Riordan and G. I. Shishkin,. 2004. Singularly perturbed convection diffusion problems with boundary and weak interior layers. Journal Of Computational And Applied Mathematics, 166, 1, pp133-151.
• P. A. Farrell, A. F. Hegarty, J. J. H. Miller, E. O' Riordan and G. I. Shishkin, ,. 2004. Singularly perturbed convection diffusion problems with boundary and weak interior layers. Journal Of Computational And Applied Mathematics, 166, , pp131-151.
• S. Bellew and E. O¿ Riordan,. 2004. A parameter-robust numerical method for a system of two singularly perturbed convection-diffusion equations. Applied Numerical Mathematics (elsevier), 51, 2-3, pp171-186.
• E. O' Riordan, M. L. Pickett and G. I. Shishkin,. 2003. Singularly perturbed problems modelling reaction-convection-diffusion processes. Computational Methods In Applied Mathematics, 3, 3, pp424-442.
• P. A. Farrell, A. F. Hegarty, J. J. H. Miller, E. O' Riordan and G. I. Shishkin,. 2003. Numerical techniques for flow problems with singularities,. International Journal For Numerical Methods In Fluids, 43, 8, pp915-936.
• R. K. Dunne, E. O' Riordan and G. I. Shishkin,. 2003. A Fitted Mesh Method for a Class of Singularly Perturbed Parabolic Problems with a Boundary Turning Point. Computational Methods In Applied Mathematics, 3, , pp361-372.
• H. MacMullen, E. O'Riordan and G.I. Shishkin,. 2002. The convergence of classical Schwarz methods applied to convection-diffusion problems with regular boundary layers,. Applied Numerical Mathematics (elsevier), 43, 3, pp297-313.
• P. A. Farrell, A. F. Hegarty, J. J. H. Miller, E. O' Riordan and G. I. Shishkin. 2002. 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. Applied Numerical Mathematics (elsevier), 40/1-4,, pp143-149.
• S. Matthews, E. O' Riordan and G. I. Shishkin,. 2002. A numerical method for a system of singularly perturbed reaction-diffusion problems. Journal Of Computational And Applied Mathematics, 145, 1, pp151-166.
• C. Clavero, J. J. H. Miller, E. O'Riordan and G.I. Shishkin. 2001. Numerical experiments for advection-diffusion problems in a channel with a 180° bend. Applied Numerical Mathematics (elsevier), 118(2-3),, pp223-246.
• C. Clavero, J. J. H. Miller, E. O'Riordan and G.I. Shishkin. 2001. Numerical experiments for advection-diffusion problems in a channel with a 180¿a bend. Applied Mathematics And Computation, 118, 2-3, pp223-246.
• H. Mac Mullen, J. J. H. Miller, E. O' Riordan and G. I. Shishkin. 2001. A second order parameter-robust overlapping Schwarz method for reaction-diffusion problems with boundary layers. Journal Of Computational And Applied Mathematics, 130/1-2,, pp231-244.
• H. Mac Mullen, J. J. H. Miller, E. O' Riordan and G. I. Shishkin,. 2001. Parameter-uniform fitted mesh method for quasilinear differential equation with boundary layers,. Computational Methods In Applied Mathematics, 2, 1-2, pp154-172.
• P. A. Farrell, J.J.H. Miller, E. O'Riordan and G.I. Shishkin. 2001. Uniformly convergent finite difference methods for singularly perturbed quasilinear differential equations. Computational Methods In Applied Mathematics, 1,, pp154-172.
• J.J.H. Miller, E. O'Riordan, G.I. Shishkin and S. Wang. 2000. A parameter-uniform Schwarz method for a singularly perturbed reaction-diffusion problem with an interior layer. Applied Numerical Mathematics (elsevier), 35(4),, pp323-337.
• J.J.H. Miller, E. O'Riordan, G.I. Shishkin and S. Wang. 2000. A parameter-uniform Schwarz method for a singularly perturbed reaction-diffusion problem with an interior layer. Applied Numerical Mathematics (elsevier), 35, 4, pp323-337.
• C. Clavero, J.J.H. Miller, E. O'Riordan and G.I. Shishkin. 1998. On the numerical solution of a two-dimensional heat transfer problem with a parabolic boundary layer. Chinese Journal Of Computational Mathematics, 16,, pp27-39.
• J.J.H. Miller, E. O'Riordan, G.I. Shishkin and L.P. Shishkina,. 1998. Fitted mesh methods for problems with parabolic boundary layers,. Mathematical Proceedings Of The Royal Irish Academy, 98A, 2, pp173-190.
• Farrell PA Miller JJH O'Riordan E Shishkin GI. 1998. On the non-existence of epsilon-uniform finite difference methods on uniform meshes for semilinear two-point boundary value problems. Mathematics Of Computation, 67,, pp603-617.
• Clavero C Miller JJH O'Riordan E Shishkin GI. 1998. An accurate numerical solution of a two dimensional heat transfer problem with a parabolic boundary layer. Journal Of Computational Mathematics, 16,, pp27-39.
• M.Stynes and E.O'Riordan. 1997. A uniformly convergent Galerkin method on a Shishkin mesh for a convection-diffusion problem. Journal Of Mathematical Analysis And Applications, 214,, pp36-54.
• P.A.Farrell, J.J.H. Miller, E. O'Riordan and G.I. Shishkin. 1996. A uniformly convergent finite difference scheme for a singularly perturbed semilinear equation. Siam Journal On Numerical Analysis, 33,3,, pp1135-1149.
• A.F.Hegarty, J.J.H.Miller, E.O'Riordan, G.I.Shishkin,. 1995. Special meshes for finite difference approximations to an advection-diffusion equation with parabolic layers,. Journal Of Computational Physics, 117, , pp47-54.
• A.F.Hegarty, J.J.H.Miller, E.O'Riordan, G.I.Shishkin,. 1995. On a novel mesh for the regular boundary layers arising in advection-dominated transport in two dimensions,. Communications In Numerical Methods In Engineering, 11, , pp435-441.
• J.J.H. Miller, E. O'Riordan and G.I. Shishkin. 1995. On piecewise-uniform meshes for upwind and central difference operators for solving singularly perturbed problems. Ima Journal Of Numerical Analysis (oxford University Pr, 15,, pp89-99.
• A.F.Hegarty, J.J.H. Miller, E. O'Riordan and G.I. Shishkin,. 1995. Numerical results for advection-dominated heat transfer in a moving fluid with a non-slip boundary condition. International Journal Of Numerical Methods For Heat And Fluid Flow, 5, 2, pp131-140.
• A.F.Hegarty, J.J.H. Miller , E. O'Riordan and G.I. Shishkin. 1994. Use of central-difference operators for the solution of singularly perturbed problems,. Communications In Numerical Methods In Engineering, 10, , pp297-302.
• A.F.Hegarty, J.J.H. Miller , E. O'Riordan and G.I. Shishkin, East-West. 1994. Special numerical methods for convection-dominated laminar flows at arbitrary Reynolds number. Journal Of Numerical Mathematics, 2, , pp65-74.
• A.F.Hegarty, E.O'Riordan, M.Stynes,. 1993. A comparison of uniformly convergent difference schemes for two-dimensional convection-diffusion problems,. Journal Of Computational Physics, 105, , pp24-32.
• E.O'Riordan and M.Stynes. 1991. A globally uniformly convergent finite element method for a singularly perturbed elliptic problem in two dimensions. Mathematics Of Computation, 57,, pp47-62.
• J.J.H.Miller, E.Mullarkey, E.O'Riordan, G.I.Shishkin,. 1991. A simple recipe for uniformly convergent finite difference schemes for singularly perturbed problems. Comptes Rendues Acad. Sc. Paris, 312, , pp643-648.
• M.Stynes and E.O'Riordan. 1991. An analysis of a singularly perturbed two-point boundary value problem using only finite element techniques. Mathematics Of Computation, 56,, pp663-675.
• M.Stynes and E.O'Riordan,. 1989. Uniformly convergent difference schemes for singularly perturbed parabolic diffusion-convection problems without turning points. Numerische Mathematik, 55, , pp521-544.
• M.J.Ng-Stynes, E.O'Riordan, M.Stynes. 1988. Numerical methods for time-dependent convection-diffusion equations. Journal Of Computational And Applied Mathematics, 21,, pp289-310.
• E.O'Riordan and M.Stynes. 1987. A uniform finite element method for a conservative singularly perturbed problem. Journal Of Computational And Applied Mathematics, 18,, pp163-174.
• M.Stynes and E.O'Riordan,. 1987. and uniform convergence of a difference scheme for a semilinear singular perturbation problem. Numerische Mathematik, 50, , pp519-532.
• E.O'Riordan. 1986. Numerical methods for singularly perturbed differential equations. Irish Mathematical Society Newsletter, 16,, pp14-24.
• M.Stynes and E.O'Riordan. 1986. A finite element method for a singularly perturbed boundary value problem. Numerische Mathematik Analysis, 50,, pp1-15.
• E.O'Riordan and M.Stynes. 1986. A uniformly accurate finite element method for a singularly perturbed one-dimensional reaction-diffusion problem. Mathematics Of Computation, 47,, pp550-570.
• M.Stynes and E.O'Riordan. 1986. A uniformly accurate finite element method for a singular perturbation problem in conservative form. Siam Journal On Numerical Analysis, 23,, pp369-375.
• E.O'Riordan and M.Stynes,. 1986. An analysis of a superconvergence result for a singularly perturbed boundary value problem,. Mathematics Of Computation, 46, , pp81-92.
• C.Fitzsimons, J.J.H.Miller, E.O'Riordan,. 1985. Petrov-Galerkin finite element methods for a hinged test space for singularly perturbed problems. International Journal For Numerical Methods In Engineering, 21, , pp1803-1812.
• Eugene O'Riordan. 1984. Singularly perturbed finite element methods. Numerische Mathematik, 44, , pp425-434.
• J.J.H.Miller, E.O'Riordan,. 1983. Hinged finite element method for two-point boundary value problems with a singular perturbation. Numerical Methods In Continuum Mechanics, 14, , pp142-154.

Selected Books

• J.J.H. Miller, Eugene O'Riordan and G.I. Shishkin. Fitted Numerical Methods for Singular perturbation problems (Revised Edition), World Scientific, 2012.
• P. A. Farrell, A. F. Hegarty, J. J. H. Miller , E. O' Riordan and G. I. Shishkin. Robust computational techniques for boundary layers, Chapman and Hall/ CRC press, 2000.
• J. J. H. Miller , E. O' Riordan and 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, 1996.

Selected Chapters

• A.F.Hegarty, J.J.H. Miller, E. O'Riordan and G.I. Shishkin. 1993. Key to the computation of the transfer of a substance by convection-diffusion in a laminar fluid. Applications of Advanced Computational Methods for Boundary and Interior Layer, Boole Press, pp94-107.
• J.J.H. Miller, E. O'Riordan, E.A. Petrenko and G.I. Shishkin. 1993. Special finite difference methods for calculating heat fields in solid bodies with rapidly changing surface temperature. Applications of Advanced Computational Methods for Boundary and Interior Layers, Boole Press,, pp108-123.
• E.O'Riordan and M.Stynes. 1991. An analysis of some exponentially fitted finite element methods for singularly perturbed elliptic problems. Computational Methods for Boundary and Interior Layers in Several Dimensions, pp138-153.

Selected Non-peer Reviewed Journals

• E.O'Riordan, , Irish Math. Soc. Bull.,. 1986. Numerical methods for singularly perturbed differential equations. , pp14-24.

• E. O' Riordan and J. Quinn, Multiscale convection in one dimensional singularly perturbed convection--diffusion problems, Fifth Conference on Numerical Analysis and Applications , 15-JUN-12 - 20-JUN-12, Lozenetz, Bulgaria.
• E. O'Riordan, A return visit to Petrov-Galerkin methods and discretized Green's functions for singularly perturbed problems, Numerical Analysis for Singularly Perturbed Problems, 16-NOV-11 - 19-NOV-11, Dresden, Germany
• E.O'Riordan and J.l. Gracia, Numerical methods for singularly perturbed reaction-diffusion problems with interior layers, European Conference on Numerical Mathematics and Advanced Applications, 05-SEP-11 - 09-SEP-11, Leicester, UK
• E.O'Riordan, Opposing flows in a one dimensional convection-diffusion problem, 9th Annual Workshop on Numerical Methods for Problems with Layer Phenomena, 03-FEB-11 - 04-FEB-11, Dublin City University, Dublin
• E.O'Riordan and J.L. Gracia, A singularly perturbed convection diffusion parabolic problem with an interior layer, BAIL 2010 - Boundary and Interior Layers, Computational and Asymptotic Mathods., 05-JUL-10 - 09-JUL-10, Zaragoza, Spain
• J.L. Gracia and E.O'Riordan, Interior layers in singularly perturbed time dependent problems, 8th Annual Workshop on Numerical Methods for Problems with Layer Phenomena, 21-JAN-10 - 22-JAN-10, University of Limerick, Ireland
• E. O'Riordan and C. de Falco, Interior layers in singularly perturbed differential equations, 23rd Biennial Conference on Numerical Analysis, 23-JUN-09 - 26-JUN-09, Glasgow, Scotland
• E.O'Riodan and M. Pickett, Two parameter singularly perturbed elliptic problems, 7th Annual Workshop on Numerical Methods for Problems with Layer Phenomena, 22-JAN-09 - 23-JAN-09, University of Limerick, Ireland
• M. Culpo, C. de Falco and E. O' Riordan, Patches of Finite Elements for Singularly-Perturbed Diffusion Reaction Equations with Discontinuous Coefficients, Progress in Industrial Mathematics at ECMI 2008, 30-JUN-08 - 04-JUL-08, London, UK
• E. O' Riordan, J. Stynes and M. Stynes, An iterative numerical algorithm for a strongly coupled system of singularly perturbed convection-diffusion problems, In: S. Margenov, L.Vulkov and J. Wasniewski ed.Numerical Analysis and Applications, 16-JUN-08 - 20-JUN-08, Lozenetz, Bulgaria., 104 - 115
• P.A. Farrell and E. O'Riordan, A class of singularly perturbed quasilinear differential equations with interior layers, 6th Annual Workshop on Numerical Methods for Problems with Layer Phenomena , 08-FEB-07 - 09-FEB-07, University of Limerick, Ireland
• Dunne R. K. and O' Riordan E., Interior layers arising in linear singularly perturbed differential equations with discontinuous coefficients, In: I. Farago, P. Vabishchevich and L.Vulkov ed.Fourth International Conference on Finite Difference Methods: Theory and Applications, 26-AUG-06 - 29-AUG-06, Lozenetz, Bulgaria, 29 - 38
• Dunne,R. K., O' Riordan, E. and Turner, M. M., A singular perturbation problem arising in the modelling of plasma sheaths, Boundary and Interior Layers, 24-JUL-06 - 28-JUL-06, Gottingen, Germany
• E.O'Riordan, Solution decomposition in the case of an elliptic problem of convection-diffusion type, 5th Annual Workshop on Numerical Methods for Problems with Layer Phenomena , 09-FEB-06 - 10-FEB-06, University of Limerick, Ireland
• C. Clavero, J.L. Gracia and E. O'Riordan,, The defect-correction technique applied to singularly perturbed elliptic problems of convection-diffusion type, Ninth International Conference Zaragoza-Pau on Applied Mathematics and Statistics , 19-SEP-05 - 21-SEP-05, Jaca, (Spain)
• R. K. Dunne, E. O' Riordan and G. I. Shishkin, ,, Numerical Methods for Singularly Perturbed Elliptic Problems with Mixed Derivatives, 10th international conference Trakai Mathematical Modelling and Analysis, 01-JUN-05 - 01-JUN-05, Lithuania, 213 - 219
• R. K. Dunne, E. O' Riordan and G. I. Shishkin,, Numerical Methods for Singularly Perturbed Elliptic Problems with Mixed Derivatives, 10th international conference on Mathematical Modelling and Analysis, 01-JUN-05 - 05-JUN-05, Trakia, Lithuania
• J.L. Gracia and E.O'Riordan, A defect-correction method for a convection-diffusion problem in one dimension, 4th Annual Workshop on Numerical Methods for Problems with Layer Phenomena , 10-FEB-05 - 11-FEB-05, University of Limerick, Ireland
• P. A. Farrell, E. O' Riordan and G. I. Shishkin,, Robust numerical methods for singularly perturbed semilinear differential equations with interior layers,, BAIL 2004 - Boundary and Interior Layers-computational and asymptotic methods, 05-JUL-04 - 09-JUL-04, Toulouse, France
• R.K. Dunne, E. O'Riordan, G.I. Shishkin, "Boundary Layers in Singularly Perturbed Problems on Non-Rectangular Domains, In: S.Wang and N.Fowkes ed.BAIL2002, 08-JUL-02 - 12-JUL-02, Perth, Western Australia, 109 - 114
• G. I. Shishkin, P. A. Farrell, A. F. Hegarty, J. J. H. Miller, E. O¿Riordan., On Reynolds-uniform numerical methods, in parabolic boundary layer regions, for Prandtl¿s problems, In: R. Ciegis, A. Samarskii and M. Sapagovas ed.3rd International Conference FDS2000, 01-SEP-00 - 04-SEP-00, Palanga, Lithuania, 215 - 225
• G. I. Shishkin, P.A. Farrell, A. F. Hegarty, J.J.H. Miller and E. O' Riordan,, On a necessary requirement for Re-uniform numerical methods to solve boundary layer equations for flow past a flat plate., In: L.Vulkov, J. Wasniewski and P.Yalamov ed.2nd International Conference NAA'2000, 11-JUN-00 - 15-JUN-00, Rousse, Bulgaria,, 723 - 731
• P.A. Farrell, A.F. Hegarty, J.J.H. Miller , E. O' Riordan and G. I. Shishkin, Parameter-uniform numerical methods for a singularly perturbed problem with a Neumann boundary condition, 2nd International Conference NAA'2000, 11-JUN-00 - 15-JUN-00, Rousse, Bulgaria
• P.A. Farrell, A.F. Hegarty, J.J.H. Miller , E. O' Riordan and G. I. Shishkin,, Parameter-uniform numerical methods for a singularly perturbed problem with a Neumann boundary condition., In: L.Vulkov, J.Wasniewski and P.Yalamov ed.2nd International Conference NAA'2000, 11-JUN-00 - 15-JUN-00, Rousse, Bulgaria, 292 - 303
• R. K. Dunne, E. O' Riordan and G. I. Shishkin, vol., Singularly perturbed parabolic problems on non-rectangular domains,, In: L.Vulkov, J.Wasniewski and P.Yalamov ed.2nd International Conference NAA'2000, 11-JUN-00 - 15-JUN-00, Rousse, Bulgaria, 265 - 272
• H. Mac Mullen, E. O' Riordan and G.I. Shishkin,, Schwarz Methods for Convection-Diffusion Problems,, In: L.Vulkov, J.Wasniewski and P.Yalamov ed.2nd International Conference NAA'2000,, 11-JUN-00 - 15-JUN-00, Rousse, Bulgaria, 554 - 551
• S. Matthews, J.J.H. Miller , E. O'Riordan and G.I. Shishkin,, A parameter robust numerical method for a system of singularly perturbed ordinary differential equations,, In: J.J.H. Miller, G.I. Shishkin and L.Vulkov ed."Analytical and Numerical Methods for Convection-Dominated and Singularly Perturbed Problems",, 27-AUG-98 - 31-AUG-98, Lozenetz, Bulgaria, 219 - 224
• P.A. Farrell, J. J. H. Miller, E. O' Riordan and G. I. Shishkin,, Singularly perturbed differential equations with discontinuous source terms,, In: J.J.H. Miller, G. I. Shishkin and L.Vulkov ed."Analytical and Numerical Methods for Convection-Dominated and Singularly Perturbed Problems", 27-AUG-98 - 31-AUG-98, Lozenetz, Bulgaria, 23 - 32
• H. Mac Mullen, J.J.H. Miller, E. O'Riordan and G.I. Shishkin, eds., 2000, pp. 213-218., Schwarz iterative method for convection-diffusion problems with boundary layers,, In: J.J.H. Miller, G.I. Shishkin and L.Vulkov ed."Analytical and Numerical Methods for Convection-Dominated and Singularly Perturbed Problems", 27-AUG-98 - 31-AUG-98, Lozenetz, Bulgaria, 213 - 218
• J.J.H. Miller, E. O'Riordan and G.I. Shishkin,, Fitted mesh methods for the singularly perturbed reaction-diffusion problem,, In: E. Minchev, ed.V-th International Conference on Numerical Analysis, 13-AUG-96 - 17-AUG-96, Plovdiv, Bulgaria, 99 - 105
• J.J.H. Miller, E. O'Riordan and G.I. Shishkin, Fitted Numerical Methods for Four Simple Convection-Diffusion Problems,, In: S. Tangmanee and E. Schulz, World Scientific ed.2nd Asian Conference on Mathematics, 17-OCT-95 - 20-OCT-95, Thailand, 444 - 448
• J.J.H. Miller, E. O'Riordan and G.I. Shishkin,, On the use of fitted operator methods for singularly perturbed partial differential equations, in "Advanced Mathematics: Computations and Applications",, In: A.S.Alekseev and N.S.Bakvalov ed.International Conference AMCA-95, 20-JUN-95 - 24-JUN-95, Novosibirsk, Russia, 518 - 531
• P.A.Farrell, A.F.Hegarty, J.J.H. Miller, E. O'Riordan and G.I. Shishkin, On the design of piecewise uniform meshes for solving advection-dominated transport equations to a prescribed accuracy in proc, 10th GAMM-Seminar , 01-JAN-94 - 01-JAN-94, Kiel, Germany, 86 - 95
• A.F.Hegarty, J.J.H. Miller, E. O'Riordan and G.I. Shishkin, On numerical experiments with central difference operators on special piecewise uniform meshes for problems with boundary layers, 9th GAMM-Seminar , 01-JAN-93 - 01-JAN-93, Kiel, Germany
• A. F. Hegarty, J.J.H. Miller, E. O'Riordan and G.I. Shishkin,, BAIL VI Procs, In: Front Range Press ed.6th International Conf. on Boundary and Interior Layers, 31-AUG-92 - 31-AUG-92, Colorado, 67 - 68
• A.F.Hegarty, J.J.H. Miller, E. O'Riordan and G.I. Shishkin., Special meshes for two dimensional elliptic singular perturbation problems, IMACS, 13th world congress on computation and applied mathematics, 22-JUL-91 - 26-JUL-91, Dublin, 503 - 504
• E.O'Riordan, A.F.Hegarty, M.Stynes,, Construction and analysis of some exponentially upwinded finite element methods for singularly perturbed two-dimensional elliptic problems,, Numerical methods in singularly perturbed problems, 18-MAR-91 - 22-MAR-91, Technische Universitat Dresden,, 91 - 96
• M.Stynes and E.O'Riordan,, Analysis of singularly perturbed two-point boundary value problems with turning points, Discretization methods in singular perturbations and flow problems, 03-APR-89 - 07-APR-89, Otto von Guericke, Magdeburg, 81 - 88
• E.O'Riordan and M.Stynes,, A uniformly convergent difference scheme for an elliptic singular perturbation problem,, Discretization methods in singular perturbations and flow problems, 03-APR-89 - 07-APR-89, Otto von Guericke,Magdeburg,, 48 - 55
• A.F.Hegarty, J.J.H.Miller, E.O'Riordan, Uniform second order difference schemes for singular perturbation problems, In: J.J.H.Miller ed.First International Conference on Boundary and Interior Layers- Computational and Asymptotic methods, 03-JUN-80 - 06-JUN-80, Dublin, 301 - 305