Finite element methods on piecewise equidistant meshes for interior turning point problems. - Guangfu Sun; Martin Stynes (Numer. Algorithms, 1994)

A Nonconforming Finite Element Method for a Singularly Petrurbed Boundary Value Problem. - Dirk Adam; Andreas Felgenhauer; Hans-Görg Roos; Martin Stynes (Computing, 1995)

A uniformly convergent method for a singularly perturbed semilinear reaction-diffusion problem with multiple solutions. - Guangfu Sun; Martin Stynes (Math. Comput., 1996)

An analysis of a cell-vertex finite volume method for a parabolic convection-diffusion problem. - Wen Guo; Martin Stynes (Math. Comput., 1997)

Analysis of a cell-vertex finite volume method for convection-diffusion problems. - K. W. Morton; Martin Stynes; Endre Süli (Math. Comput., 1997)

A finite difference analysis of a streamline diffusion method on a Shishkin mesh. - Martin Stynes; Lutz Tobiska (Numer. Algorithms, 1998)

Analysis of the streamline-diffusion finite element method on a piecewise uniform mesh for a convection-diffusion problem with exponential layers. - Martin Stynes; Lutz Tobiska (J. Num. Math., 2001)

The sdfem on Shishkin meshes for linear convection-diffusion problems. - Torsten Linß; Martin Stynes (Numerische Mathematik, 2001)

n-Widths and Singularly Perturbed Boundary Value Problems II. - R. Bruce Kellogg; Martin Stynes (SIAM J. Numer. Anal., 2001)

A Robust Adaptive Method for a Quasi-Linear One-Dimensional Convection-Diffusion Problem. - Natalia Kopteva; Martin Stynes (SIAM J. Numer. Anal., 2001)

The SDFEM for a Convection-Diffusion Problem with a Boundary Layer: Optimal Error Analysis and Enhancement of Accuracy. - Martin Stynes; Lutz Tobiska (SIAM J. Numer. Anal., 2003)

Grid equidistribution for reaction-diffusion problems in one dimension. - Natalia Kopteva; Niall Madden; Martin Stynes (Numer. Algorithms, 2005)

Numerical analysis of singularly perturbed nonlinear reaction-diffusion problems with multiple solutions. - Martin Stynes; Natalia Kopteva (Comput. Math. Appl., 2006)

Sharpened bounds for corner singularities and boundary layers in a simple convection-diffusion problem. - R. Bruce Kellogg; Martin Stynes (Appl. Math. Lett., 2007)

Convection-diffusion-reaction problems, SDFEM/SUPG and a priori meshes. - Martin Stynes (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)

A finite difference method on layer-adapted meshes for an elliptic reaction-diffusion system in two dimensions. - R. Bruce Kellogg; Torsten Linß; Martin Stynes (Math. Comput., 2008)

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

Numerical Solution of Systems of Singularly Perturbed Differential Equations. - Torsten Linß; Martin Stynes (Comput. Methods Appl. Math., 2009)

Singularly Perturbed Convection - Diffusion Problems in One Dimension: Bounds on Derivatives. - Aidan Naughton; Martin Stynes (Comput. Methods Appl. Math., 2009)

A simpler analysis of a hybrid numerical method for time-dependent convection-diffusion problems. - Carmelo Clavero; Jose L. Gracia; Martin Stynes (J. Comput. Appl. Math., 2011)

Stabilised approximation of interior-layer solutions of a singularly perturbed semilinear reaction-diffusion problem. - Natalia Kopteva; Martin Stynes (Numerische Mathematik, 2011)

Postprocessed Two-Scale Finite Element Discretizations, Part I. - Fang Liu; Martin Stynes; Aihui Zhou (SIAM J. Numer. Anal., 2011)

Galerkin and streamline diffusion finite element methods on a Shishkin mesh for a convection-diffusion problem with corner singularities. - Sebastian Franz; R. Bruce Kellogg; Martin Stynes (Math. Comput., 2012)

A Balanced Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems. - Runchang Lin; Martin Stynes (SIAM J. Numer. Anal., 2012)

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

Some Open Questions in the Numerical Analysis of Singularly Perturbed Differential Equations. - Hans-Görg Roos; Martin Stynes (Comput. Methods Appl. Math., 2015)

Boundary Layers in a Two-Point Boundary Value Problem with a Caputo Fractional Derivative. - Martin Stynes; José Luis Gracia (Comput. Methods Appl. Math., 2015)

Central difference approximation of convection in Caputo fractional derivative two-point boundary value problems. - Jose L. Gracia; Martin Stynes (J. Comput. Appl. Math., 2015)

A balanced finite element method for a system of singularly perturbed reaction-diffusion two-point boundary value problems. - Runchang Lin; Martin Stynes (Numer. Algorithms, 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)

A spectral collocation method for a weakly singular Volterra integral equation of the second kind. - Can Huang; Martin Stynes (Adv. Comput. Math., 2016)

Analysis and numerical solution of a Riemann-Liouville fractional derivative two-point boundary value problem. - Natalia Kopteva; Martin Stynes (Adv. Comput. Math., 2017)

Preprocessing schemes for fractional-derivative problems to improve their convergence rates. - Martin Stynes; José Luis Gracia (Appl. Math. Lett., 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)

A High Order Method on Graded Meshes for a Time-Fractional Diffusion Problem. - Hu Chen 001; Martin Stynes (FDM, 2018)

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

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)

Optimal uniform-convergence results for convection-diffusion problems in one dimension using preconditioning. - Thái Anh Nhan; Martin Stynes; Relja Vulanovic (J. Comput. 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)

Collocation Methods for General Caputo Two-Point Boundary Value Problems. - Hui Liang 001; Martin Stynes (J. Sci. Comput., 2018)

Collocation methods for general Riemann-Liouville two-point boundary value problems. - Hui Liang 001; Martin Stynes (Adv. Comput. Math., 2019)

Convergence analysis of the Adini element on a Shishkin mesh for a singularly perturbed fourth-order problem in two dimensions. - Xiangyun Meng; Martin Stynes (Adv. Comput. Math., 2019)

Balanced-norm error estimates for sparse grid finite element methods applied to singularly perturbed reaction-diffusion problems. - Stephen Russell; Martin Stynes (J. Num. Math., 2019)

Error Analysis of a Second-Order Method on Fitted Meshes for a Time-Fractional Diffusion Problem. - Hu Chen 001; Martin Stynes (J. Sci. Comput., 2019)

Optimal H1 spatial convergence of a fully discrete finite element method for the time-fractional Allen-Cahn equation. - Chaobao Huang; Martin Stynes (Adv. Comput. Math., 2020)

A discrete comparison principle for the time-fractional diffusion equation. - Hu Chen 001; Martin Stynes (Comput. Math. Appl., 2020)

Error analysis of a finite element method with GMMP temporal discretisation for a time-fractional diffusion equation. - Chaobao Huang; Martin Stynes (Comput. Math. Appl., 2020)

Error Analysis of a Finite Difference Method on Graded Meshes for a Multiterm Time-Fractional Initial-Boundary Value Problem. - Chaobao Huang; Xiaohui Liu; Xiangyun Meng; Martin Stynes (Comput. Methods Appl. Math., 2020)

Optimal spatial H1-norm analysis of a finite element method for a time-fractional diffusion equation. - Chaobao Huang; Martin Stynes (J. Comput. Appl. Math., 2020)

Superconvergence of a Finite Element Method for the Multi-term Time-Fractional Diffusion Problem. - Chaobao Huang; Martin Stynes (J. Sci. Comput., 2020)

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

A direct discontinuous Galerkin finite element method for convection-dominated two-point boundary value problems. - Guanglong Ma; Martin Stynes (Numer. Algorithms, 2020)

An α-robust finite difference method for a time-fractional radially symmetric diffusion problem. - Lin Wang; Martin Stynes (Comput. Math. Appl., 2021)

Two Finite Difference Schemes for Multi-Dimensional Fractional Wave Equations with Weakly Singular Solutions. - Jinye Shen; Martin Stynes; Zhi-Zhong Sun (Comput. Methods Appl. Math., 2021)

A finite difference method for an initial-boundary value problem with a Riemann-Liouville-Caputo spatial fractional derivative. - José Luis Gracia; Martin Stynes (J. Comput. Appl. Math., 2021)

An α-robust finite element method for a multi-term time-fractional diffusion problem. - Chaobao Huang; Martin Stynes; Hu Chen 001 (J. Comput. Appl. Math., 2021)

An α-Robust Semidiscrete Finite Element Method for a Fokker-Planck Initial-Boundary Value Problem with Variable-Order Fractional Time Derivative. - Kim-Ngan Le; Martin Stynes (J. Sci. Comput., 2021)

α-robust error analysis of a mixed finite element method for a time-fractional biharmonic equation. - Chaobao Huang; Martin Stynes (Numer. Algorithms, 2021)

Using Complete Monotonicity to Deduce Local Error Estimates for Discretisations of a Multi-Term Time-Fractional Diffusion Equation. - Hu Chen 001; Martin Stynes (Comput. Methods Appl. Math., 2022)

Optimal long-time decay rate of solutions of complete monotonicity-preserving schemes for nonlinear time-fractional evolutionary equations. - Dongling Wang; Martin Stynes (CoRR, 2022)

Block boundary value methods for solving linear neutral Volterra integro-differential equations with weakly singular kernels. - Yongtao Zhou; Martin Stynes (J. Comput. Appl. Math., 2022)

A Sharp α-Robust L∞ (H1) Error Bound for a Time-Fractional Allen-Cahn Problem Discretised by the Alikhanov L2-1σ Scheme and a Standard FEM. - Chaobao Huang; Martin Stynes (J. Sci. Comput., 2022)

A Posteriori Error Analysis for Variable-Coefficient Multiterm Time-Fractional Subdiffusion Equations. - Natalia Kopteva; Martin Stynes (J. Sci. Comput., 2022)

Balanced-Norm and Energy-Norm Error Analyses for a Backward Euler/FEM Solving a Singularly Perturbed Parabolic Reaction-Diffusion Problem. - Xiangyun Meng; Martin Stynes (J. Sci. Comput., 2022)

A sharp discrete convolution sum estimate. - Martin Stynes; Dongling Wang (Commun. Nonlinear Sci. Numer. Simul., 2023)

Supercloseness of the local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem. - Yao Cheng; Shan Jiang; Martin Stynes (Math. Comput., 2023)

Discretised general fractional derivative. - Enyu Fan; Changpin Li; Martin Stynes (Math. Comput. Simul., 2023)

The local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem with characteristic and exponential layers. - Yao Cheng; Martin Stynes (Numerische Mathematik, 2023)

Optimal Long-Time Decay Rate of Numerical Solutions for Nonlinear Time-Fractional Evolutionary Equations. - Dongling Wang; Martin Stynes (SIAM J. Numer. Anal., 2023)

A collocation method for an RLC fractional derivative two-point boundary value problem with a singular solution. - José Luis Gracia; Martin Stynes (Comput. Appl. Math., 2024)

An α-robust error analysis of the L1‾ scheme for time-fractional integro-differential initial-boundary value problems. - Yongtao Zhou; Hongyu Qin; Martin Stynes (Comput. Math. Appl., 2024)

Optimal balanced-norm error estimate of the LDG method for reaction-diffusion problems II: the two-dimensional case with layer-upwind flux. - Yao Cheng; Xuesong Wang; Martin Stynes (CoRR, 2024)

A fast second-order predictor-corrector method for a nonlinear time-fractional Benjamin-Bona-Mahony-Burgers equation. - Yongtao Zhou; Cui Li; Martin Stynes (Numer. Algorithms, 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. - Xiangyun Meng; Martin Stynes (Numer. Algorithms, 2024)

Error analysis of a collocation method on graded meshes for a fractional Laplacian problem. - Minghua Chen 002; Weihua Deng; Chao Min; Jiankang Shi; Martin Stynes (Adv. Comput. Math., 2024)

Optimal Balanced-Norm Error Estimate of the LDG Method for Reaction-Diffusion Problems I: The One-Dimensional Case. - Yao Cheng; Xuesong Wang; Martin Stynes (J. Sci. Comput., 2024)

Sharp Error Bounds for a Fractional Collocation Method for Weakly Singular Volterra Integral Equations with Variable Exponent. - Zheng Ma; Martin Stynes (J. Sci. Comput., 2024)

A Nyström method based on product integration for weakly singular Volterra integral equations with variable exponent. - Zheng Ma; Martin Stynes (J. Comput. Appl. Math., 2025)