Martin Stynes

Orcid: 0000-0003-2085-7354

According to our database1, Martin Stynes authored at least 79 papers between 1994 and 2025.

Collaborative distances:
  • Dijkstra number2 of five.
  • Erdős number3 of four.

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Bibliography

2025
A Nyström method based on product integration for weakly singular Volterra integral equations with variable exponent.
J. Comput. Appl. Math., 2025

2024
Sharp Error Bounds for a Fractional Collocation Method for Weakly Singular Volterra Integral Equations with Variable Exponent.
J. Sci. Comput., August, 2024

Optimal Balanced-Norm Error Estimate of the LDG Method for Reaction-Diffusion Problems I: The One-Dimensional Case.
J. Sci. Comput., August, 2024

Error analysis of a collocation method on graded meshes for a fractional Laplacian problem.
Adv. Comput. Math., June, 2024

Balanced and energy norm error bounds for a spatial FEM with Crank-Nicolson and BDF2 time discretisation applied to a singularly perturbed reaction-diffusion problem.
Numer. Algorithms, March, 2024

A fast second-order predictor-corrector method for a nonlinear time-fractional Benjamin-Bona-Mahony-Burgers equation.
Numer. Algorithms, February, 2024

Optimal balanced-norm error estimate of the LDG method for reaction-diffusion problems II: the two-dimensional case with layer-upwind flux.
CoRR, 2024

An α-robust error analysis of the L1‾ scheme for time-fractional integro-differential initial-boundary value problems.
Comput. Math. Appl., 2024

A collocation method for an RLC fractional derivative two-point boundary value problem with a singular solution.
Comput. Appl. Math., 2024

2023
Optimal Long-Time Decay Rate of Numerical Solutions for Nonlinear Time-Fractional Evolutionary Equations.
SIAM J. Numer. Anal., October, 2023

The local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem with characteristic and exponential layers.
Numerische Mathematik, June, 2023

Discretised general fractional derivative.
Math. Comput. Simul., June, 2023

Supercloseness of the local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem.
Math. Comput., April, 2023

A sharp discrete convolution sum estimate.
Commun. Nonlinear Sci. Numer. Simul., 2023

2022
Balanced-Norm and Energy-Norm Error Analyses for a Backward Euler/FEM Solving a Singularly Perturbed Parabolic Reaction-Diffusion Problem.
J. Sci. Comput., 2022

A Posteriori Error Analysis for Variable-Coefficient Multiterm Time-Fractional Subdiffusion Equations.
J. Sci. Comput., 2022

A Sharp α-Robust L<sup>∞</sup> (H<sup>1)</sup> Error Bound for a Time-Fractional Allen-Cahn Problem Discretised by the Alikhanov L2-1<sub>σ</sub> Scheme and a Standard FEM.
J. Sci. Comput., 2022

Block boundary value methods for solving linear neutral Volterra integro-differential equations with weakly singular kernels.
J. Comput. Appl. Math., 2022

Optimal long-time decay rate of solutions of complete monotonicity-preserving schemes for nonlinear time-fractional evolutionary equations.
CoRR, 2022

Using Complete Monotonicity to Deduce Local Error Estimates for Discretisations of a Multi-Term Time-Fractional Diffusion Equation.
Comput. Methods Appl. Math., 2022

2021
α-robust error analysis of a mixed finite element method for a time-fractional biharmonic equation.
Numer. Algorithms, 2021

An α-Robust Semidiscrete Finite Element Method for a Fokker-Planck Initial-Boundary Value Problem with Variable-Order Fractional Time Derivative.
J. Sci. Comput., 2021

An α-robust finite element method for a multi-term time-fractional diffusion problem.
J. Comput. Appl. Math., 2021

A finite difference method for an initial-boundary value problem with a Riemann-Liouville-Caputo spatial fractional derivative.
J. Comput. Appl. Math., 2021

Two Finite Difference Schemes for Multi-Dimensional Fractional Wave Equations with Weakly Singular Solutions.
Comput. Methods Appl. Math., 2021

An <i>α</i>-robust finite difference method for a time-fractional radially symmetric diffusion problem.
Comput. Math. Appl., 2021

2020
A direct discontinuous Galerkin finite element method for convection-dominated two-point boundary value problems.
Numer. Algorithms, 2020

Barrier Function Local and Global Analysis of an L1 Finite Element Method for a Multiterm Time-Fractional Initial-Boundary Value Problem.
J. Sci. Comput., 2020

Superconvergence of a Finite Element Method for the Multi-term Time-Fractional Diffusion Problem.
J. Sci. Comput., 2020

Optimal spatial H1-norm analysis of a finite element method for a time-fractional diffusion equation.
J. Comput. Appl. Math., 2020

Error Analysis of a Finite Difference Method on Graded Meshes for a Multiterm Time-Fractional Initial-Boundary Value Problem.
Comput. Methods Appl. Math., 2020

Error analysis of a finite element method with GMMP temporal discretisation for a time-fractional diffusion equation.
Comput. Math. Appl., 2020

A discrete comparison principle for the time-fractional diffusion equation.
Comput. Math. Appl., 2020

Optimal H<sup>1</sup> spatial convergence of a fully discrete finite element method for the time-fractional Allen-Cahn equation.
Adv. Comput. Math., 2020

2019
Error Analysis of a Second-Order Method on Fitted Meshes for a Time-Fractional Diffusion Problem.
J. Sci. Comput., 2019

Balanced-norm error estimates for sparse grid finite element methods applied to singularly perturbed reaction-diffusion problems.
J. Num. Math., 2019

Convergence analysis of the Adini element on a Shishkin mesh for a singularly perturbed fourth-order problem in two dimensions.
Adv. Comput. Math., 2019

Collocation methods for general Riemann-Liouville two-point boundary value problems.
Adv. Comput. Math., 2019

2018
Collocation Methods for General Caputo Two-Point Boundary Value Problems.
J. Sci. Comput., 2018

A Fitted Scheme for a Caputo Initial-Boundary Value Problem.
J. Sci. Comput., 2018

Optimal uniform-convergence results for convection-diffusion problems in one dimension using preconditioning.
J. Comput. Appl. Math., 2018

Convergence in Positive Time for a Finite Difference Method Applied to a Fractional Convection-Diffusion Problem.
Comput. Methods Appl. Math., 2018

Fractional-order derivatives defined by continuous kernels are too restrictive.
Appl. Math. Lett., 2018

A High Order Method on Graded Meshes for a Time-Fractional Diffusion Problem.
Proceedings of the Finite Difference Methods. Theory and Applications, 2018

2017
Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation.
SIAM J. Numer. Anal., 2017

Preprocessing schemes for fractional-derivative problems to improve their convergence rates.
Appl. Math. Lett., 2017

Analysis and numerical solution of a Riemann-Liouville fractional derivative two-point boundary value problem.
Adv. Comput. Math., 2017

2016
A spectral collocation method for a weakly singular Volterra integral equation of the second kind.
Adv. Comput. Math., 2016

Convergence Outside the Initial Layer for a Numerical Method for the Time-Fractional Heat Equation.
Proceedings of the Numerical Analysis and Its Applications - 6th International Conference, 2016

2015
A balanced finite element method for a system of singularly perturbed reaction-diffusion two-point boundary value problems.
Numer. Algorithms, 2015

Central difference approximation of convection in Caputo fractional derivative two-point boundary value problems.
J. Comput. Appl. Math., 2015

Boundary Layers in a Two-Point Boundary Value Problem with a Caputo Fractional Derivative.
Comput. Methods Appl. Math., 2015

Some Open Questions in the Numerical Analysis of Singularly Perturbed Differential Equations.
Comput. Methods Appl. Math., 2015

2014
Sharp anisotropic interpolation error estimates for rectangular Raviart-Thomas elements.
Math. Comput., 2014

2012
A Balanced Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems.
SIAM J. Numer. Anal., 2012

Galerkin and streamline diffusion finite element methods on a Shishkin mesh for a convection-diffusion problem with corner singularities.
Math. Comput., 2012

2011
Postprocessed Two-Scale Finite Element Discretizations, Part I.
SIAM J. Numer. Anal., 2011

Stabilised approximation of interior-layer solutions of a singularly perturbed semilinear reaction-diffusion problem.
Numerische Mathematik, 2011

A simpler analysis of a hybrid numerical method for time-dependent convection-diffusion problems.
J. Comput. Appl. Math., 2011

2009
Singularly Perturbed Convection - Diffusion Problems in One Dimension: Bounds on Derivatives.
Comput. Methods Appl. Math., 2009

Numerical Solution of Systems of Singularly Perturbed Differential Equations.
Comput. Methods Appl. Math., 2009

Numerical analysis of a strongly coupled system of two singularly perturbed convection-diffusion problems.
Adv. Comput. Math., 2009

2008
A finite difference method on layer-adapted meshes for an elliptic reaction-diffusion system in two dimensions.
Math. Comput., 2008

An Iterative Numerical Algorithm for a Strongly Coupled System of Singularly Perturbed Convection-Diffusion Problems.
Proceedings of the Numerical Analysis and Its Applications, 4th International Conference, 2008

2007
Convection-diffusion-reaction problems, SDFEM/SUPG and a priori meshes.
Int. J. Comput. Sci. Math., 2007

Sharpened bounds for corner singularities and boundary layers in a simple convection-diffusion problem.
Appl. Math. Lett., 2007

2006
Numerical analysis of singularly perturbed nonlinear reaction-diffusion problems with multiple solutions.
Comput. Math. Appl., 2006

2005
Grid equidistribution for reaction-diffusion problems in one dimension.
Numer. Algorithms, 2005

2003
The SDFEM for a Convection-Diffusion Problem with a Boundary Layer: Optimal Error Analysis and Enhancement of Accuracy.
SIAM J. Numer. Anal., 2003

2001
A Robust Adaptive Method for a Quasi-Linear One-Dimensional Convection-Diffusion Problem.
SIAM J. Numer. Anal., 2001

<i>n</i>-Widths and Singularly Perturbed Boundary Value Problems II.
SIAM J. Numer. Anal., 2001

The sdfem on Shishkin meshes for linear convection-diffusion problems.
Numerische Mathematik, 2001

Analysis of the streamline-diffusion finite element method on a piecewise uniform mesh for a convection-diffusion problem with exponential layers.
J. Num. Math., 2001

1998
A finite difference analysis of a streamline diffusion method on a Shishkin mesh.
Numer. Algorithms, 1998

1997
Analysis of a cell-vertex finite volume method for convection-diffusion problems.
Math. Comput., 1997

An analysis of a cell-vertex finite volume method for a parabolic convection-diffusion problem.
Math. Comput., 1997

1996
A uniformly convergent method for a singularly perturbed semilinear reaction-diffusion problem with multiple solutions.
Math. Comput., 1996

1995
A Nonconforming Finite Element Method for a Singularly Petrurbed Boundary Value Problem.
Computing, 1995

1994
Finite element methods on piecewise equidistant meshes for interior turning point problems.
Numer. Algorithms, 1994


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