On the non-existence of epsilon-uniform finite difference methods on uniform meshes for semilinear two-point boundary value problems. - Paul A. Farrell; John J. H. Miller; Eugene O'Riordan; Grigorii I. Shishkin (Math. Comput., 1998)

Singularity Perturbed Parabolic Problems on Non-rectangular Domains. - R. K. Dunne; Eugene O'Riordan; Grigorii I. Shishkin (NAA, 2000)

Parameter-Uniform Numerical Methods for a Class of Singularity Perturbed Problems with a Neumann Boundary Condition. - Paul A. Farrell; Alan F. Hegarty; John J. H. Miller; Eugene O'Riordan; Grigorii I. Shishkin (NAA, 2000)

Schwarz Methods for Convection-Diffusion Problems. - H. MacMullen; Eugene O'Riordan; Grigorii I. Shishkin (NAA, 2000)

On a Necessary Requirement for Re-Uniform Numerical Methods to Solve Boundary Layer Equations for Flow along a Flat Plate. - Grigorii I. Shishkin; Paul A. Farrell; Alan F. Hegarty; John J. H. Miller; Eugene O'Riordan (NAA, 2000)

Numerical experiments for advection-diffusion problems in a channel with a 180° bend. - Carmelo Clavero; John J. H. Miller; Eugene O'Riordan; Grigorii I. Shishkin (Appl. Math. Comput., 2001)

Global maximum norm parameter-uniform numerical method for a singularly perturbed convection-diffusion problem with discontinuous convection coefficient. - Paul A. Farrell; Alan F. Hegarty; John J. H. Miller; Eugene O'Riordan; Grigorii I. Shishkin (Math. Comput. Model., 2004)

A parameter robust numerical method for a two dimensional reaction-diffusion problem. - Carmelo Clavero; Jose L. Gracia; Eugene O'Riordan (Math. Comput., 2005)

A class of singularly perturbed semilinear differential equations with interior layers. - Paul A. Farrell; Eugene O'Riordan; Grigorii I. Shishkin (Math. Comput., 2005)

Parameter-uniform finite difference schemes for singularly perturbed parabolic diffusion-convection-reaction problems. - Eugene O'Riordan; M. L. Pickett; Grigorii I. Shishkin (Math. Comput., 2006)

A defect-correction parameter-uniform numerical method for a singularly perturbed convection-diffusion problem in one dimension. - Jose L. Gracia; Eugene O'Riordan (Numer. Algorithms, 2006)

A numerical method for a singular perturbation problem arising in the modelling of plasma sheaths. - R. K. Dunne; Eugene O'Riordan; M. M. Turner (Int. J. Comput. Sci. Math., 2007)

An Iterative Numerical Algorithm for a Strongly Coupled System of Singularly Perturbed Convection-Diffusion Problems. - Eugene O'Riordan; Jeanne Stynes; Martin Stynes (NAA, 2008)

Numerical analysis of a strongly coupled system of two singularly perturbed convection-diffusion problems. - Eugene O'Riordan; Martin Stynes (Adv. Comput. Math., 2009)

A class of singularly perturbed quasilinear differential equations with interior layers. - Paul A. Farrell; Eugene O'Riordan; Grigorii I. Shishkin (Math. Comput., 2009)

A coupled system of singularly perturbed parabolic reaction-diffusion equations. - Jose L. Gracia; Francisco Javier Lisbona; Eugene O'Riordan (Adv. Comput. Math., 2010)

A parameter-uniform numerical method for a singularly perturbed two parameter elliptic problem. - Eugene O'Riordan; M. L. Pickett (Adv. Comput. Math., 2011)

A parameter robust Petrov-Galerkin scheme for advection-diffusion-reaction equations. - Carlo de Falco; Eugene O'Riordan (Numer. Algorithms, 2011)

A Singularly Perturbed Reaction-Diffusion Problem with Incompatible Boundary-Initial Data. - Jose L. Gracia; Eugene O'Riordan (NAA, 2012)

Multiscale Convection in One Dimensional Singularly Perturbed Convection-Diffusion Problems. - Eugene O'Riordan; Jason Quinn (NAA, 2012)

Numerical Experiments with a Shishkin Numerical Method for a Singularly Perturbed Quasilinear Parabolic Problem with an Interior Layer. - Eugene O'Riordan; Jason Quinn (NAA, 2012)

A singularly perturbed parabolic problem with a layer in the initial condition. - Jose L. Gracia; Eugene O'Riordan (Appl. Math. Comput., 2012)

A Singularly Perturbed Convection Diffusion Turning Point Problem with an Interior Layer. - Eugene O'Riordan; Jason Quinn (Comput. Methods Appl. Math., 2012)

Parameter-uniform numerical methods for some singularly perturbed nonlinear initial value problems. - Eugene O'Riordan; Jason Quinn (Numer. Algorithms, 2012)

Numerical approximation of solution derivatives in the case of singularly perturbed time dependent reaction-diffusion problems. - Jose L. Gracia; Eugene O'Riordan (J. Comput. Appl. Math., 2015)

Convergence Outside the Initial Layer for a Numerical Method for the Time-Fractional Heat Equation. - José Luis Gracia; Eugene O'Riordan; Martin Stynes (NAA, 2016)

Numerical approximation of solution derivatives of singularly perturbed parabolic problems of convection-diffusion type. - Jose L. Gracia; Eugene O'Riordan (Math. Comput., 2016)

Parameter-uniform numerical method for singularly perturbed convection-diffusion problem on a circular domain. - Alan F. Hegarty; Eugene O'Riordan (Adv. Comput. Math., 2017)

A singularly perturbed convection-diffusion problem with a moving pulse. - Jose L. Gracia; Eugene O'Riordan (J. Comput. Appl. Math., 2017)

Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation. - Martin Stynes; Eugene O'Riordan; José Luis Gracia (SIAM J. Numer. Anal., 2017)

Convergence in Positive Time for a Finite Difference Method Applied to a Fractional Convection-Diffusion Problem. - José Luis Gracia; Eugene O'Riordan; Martin Stynes (Comput. Methods Appl. Math., 2018)

A Fitted Scheme for a Caputo Initial-Boundary Value Problem. - Jose L. Gracia; Eugene O'Riordan; Martin Stynes (J. Sci. Comput., 2018)

A parameter-uniform numerical method for a singularly perturbed convection-diffusion problem posed on an annulus. - Alan F. Hegarty; Eugene O'Riordan (Comput. Math. Appl., 2019)

Numerical approximations to the scaled first derivatives of the solution to a two parameter singularly perturbed problem. - Eugene O'Riordan; M. L. Pickett (J. Comput. Appl. Math., 2019)

Parameter-uniform approximations for a singularly perturbed convection-diffusion problem with a discontinuous initial condition. - José Luis Gracia; Eugene O'Riordan (CoRR, 2020)

Singularly perturbed reaction-diffusion problems with discontinuities in the initial and/or the boundary data. - José Luis Gracia; Eugene O'Riordan (J. Comput. Appl. Math., 2020)

Parameter-uniform numerical methods for singularly perturbed linear transport problems. - Jose L. Gracia; Adrián Navas-Montilla; Eugene O'Riordan (CoRR, 2021)

Numerical approximations to a singularly perturbed convection-diffusion problem with a discontinuous initial condition. - José Luis Gracia; Eugene O'Riordan (Numer. Algorithms, 2021)

A singularly perturbed convection-diffusion parabolic problem with incompatible boundary/initial data. - José Luis Gracia; Eugene O'Riordan (CoRR, 2022)

A numerical algorithm to computationally solve the Hemker problem using Shishkin meshes. - Alan F. Hegarty; Eugene O'Riordan (J. Comput. Appl. Math., 2022)

A Numerical Method for Singularly Perturbed Convection-diffusion Problems Posed on Smooth Domains. - Alan F. Hegarty; Eugene O'Riordan (J. Sci. Comput., 2022)

Fitted finite element methods for singularly perturbed elliptic problems of convection-diffusion type. - Alan F. Hegarty; Eugene O'Riordan (CoRR, 2023)

A higher order numerical method for singularly perturbed elliptic problems with characteristic boundary layers. - Alan F. Hegarty; Eugene O'Riordan (CoRR, 2023)

Singularly perturbed elliptic problems of convection-diffusion type with non-smooth inflow/outflow boundary conditions. - José Luis Gracia; Eugene O'Riordan (J. Comput. Appl. Math., 2024)