42 citations · 46 across the 13 of their papers we have counts for
13 papers
A fitted scheme for a Caputo initial-boundary value problem
J. L. Gracia, E. O'Riordan, M. Stynes
In this paper we consider an initial-boundary value problem with a Caputo time derivative of order . The solution typically exhibits a weak singularity near the initial…
A higher order numerical method for singularly perturbed elliptic problems with characteristic boundary layers
Alan F. Hegarty, Eugene O'Riordan
A Petrov-Galerkin finite element method is constructed for a singularly perturbed elliptic problem in two space dimensions. The solution contains a regular boundary layer and two c…
Fitted finite element methods for singularly perturbed elliptic problems of convection-diffusion type
Alan F. Hegarty, Eugene O'Riordan
Fitted finite element methods are constructed for a singularly perturbed convection-diffusion problem in two space dimensions. Exponential splines as basis functions are combined w…
A singularly perturbed convection-diffusion parabolic problem with incompatible boundary/initial data
Jose Luis Gracia, Eugene O'Riordan
A singularly perturbed parabolic problem of convection-diffusion type with incompatible inflow boundary and initial conditions is examined. In the case of constant coefficients, a…
A numerical method for singularly perturbed convection-diffusion problems posed on smooth domains
Alan F. Hegarty, Eugene O'Riordan
A finite difference method is constructed to solve singularly perturbed convection-diffusion problems posed on smooth domains. Constraints are imposed on the data so that only regu…
Parameter-uniform numerical methods for singularly perturbed linear transport problems
J. L. Gracia, A. Navas-Montilla, E. O'Riordan
Pointwise accurate numerical methods are constructed and analysed for three classes of singularly perturbed first order transport problems. The methods involve piecewise-uniform Sh…
Parameter-uniform approximations for a singularly perturbed convection-diffusion problem with a discontinuous initial condition
Jose Luis Gracia, Eugene O'Riordan
A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. A particular complimentary error function is identified wh…
Numerical approximations to a singularly perturbed convection-diffusion problem with a discontinuous initial condition
Jose Luis Gracia, Eugene O'Riordan
A singularly perturbed parabolic problem of convection-diffusion type with a discontinuous initial condition is examined. An analytic function is identified which matches the disco…
A numerical algorithm to computationally solve the Hemker problem using Shishkin meshes
Alan F. Hegarty, Eugene O'Riordan
A numerical algorithm is presented to solve a benchmark problem proposed by Hemker. The algorithm incorporates asymptotic information into the design of appropriate piecewise-unifo…
Singularly perturbed reaction-diffusion problems with discontinuities in the initial and/or the boundary data
Jose Luis Gracia, Eugene O'Riordan
Numerical approximations to the solutions of three different problem classes of singularly perturbed parabolic reaction-diffusion problems, each with a discontinuity in the bound\-…
Parameter-uniform numerical methods for singularly perturbed parabolic problems with incompatible boundary-initial data
Jose Luis Gracia, Eugene O'Riordan
Numerical approximations to the solution of a linear singularly perturbed parabolic reaction-diffusion problem with incompatible bound\-ary-initial data are generated, The method i…
A singularly perturbed convection-diffusion problem posed on an annulus
Alan F. Hegarty, Eugene O'Riordan
A finite difference method is constructed for a singularly perturbed convection diffusion problem posed on an annulus. The method involves combining polar coordinates, an upwind fi…
Numerical approximations to the scaled first derivatives of a two parameter singularly perturbed problem
Eugene O'Riordan, Maria Pickett
A singularly perturbed problem involving two singular perturbation parameters is discretized using the classical upwinded finite difference scheme on an appropriate piecewise-unifo…