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A Survey of the L1 Scheme in the Discretisation of Time-Fractional Problems

Numerical Mathematics: Theory, Methods and Applications, 2022-11, Vol.15 (4), p.1173-1192

Martin Stynes, Martin Stynes

2022

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ERROR ANALYSIS OF A FINITE DIFFERENCE METHOD ON GRADED MESHES FOR A TIME-FRACTIONAL DIFFUSION EQUATION

SIAM journal on numerical analysis, 2017-01, Vol.55 (2), p.1057-1079

2017

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Sharp anisotropic interpolation error estimates for rectangular Raviart-Thomas elements

Mathematics of computation, 2014-11, Vol.83 (290), p.2675-2689

STYNES, MARTIN

2014

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Steady-state convection-diffusion problems

Acta numerica, 2005-05, Vol.14, p.445-508

Stynes, Martin

2005

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Supercloseness of the local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem

Mathematics of computation, 2023-09, Vol.92 (343), p.2065-2095

2023

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An Alternative Finite Difference Stability Analysis for a Multiterm Time-Fractional Initial-Boundary Value Problem

East Asian journal on applied mathematics, 2020-08, Vol.10 (3), p.427-436

2020

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Too Much Regularity May Force Too Much Uniqueness

Fractional calculus & applied analysis, 2016-12, Vol.19 (6), p.1554-1562

Stynes, Martin

2016

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Fractional-order derivatives defined by continuous kernels are too restrictive

Applied mathematics letters, 2018-11, Vol.85, p.22-26

Stynes, Martin

2018

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Good (and Not So Good) Practices in Computational Methods for Fractional Calculus

Mathematics (Basel), 2020-03, Vol.8 (3), p.324

2020

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Error Analysis of a Second-Order Method on Fitted Meshes for a Time-Fractional Diffusion Problem

Journal of scientific computing, 2019-04, Vol.79 (1), p.624-647

2019

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Blow-up of error estimates in time-fractional initial-boundary value problems

IMA journal of numerical analysis, 2021-04, Vol.41 (2), p.974-997

2021

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Optimal spatial H 1 -norm analysis of a finite element method for a time-fractional diffusion equation

Journal of computational and applied mathematics, 2020-03, Vol.367, p.112435, Article 112435

2020

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A Nyström method based on product integration for weakly singular Volterra integral equations with variable exponent

Journal of computational and applied mathematics, 2025-01, Vol.454, p.116164, Article 116164

2025

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α-robust error analysis of a mixed finite element method for a time-fractional biharmonic equation

Numerical algorithms, 2021-08, Vol.87 (4), p.1749-1766

2021

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Superconvergence of a Finite Element Method for the Multi-term Time-Fractional Diffusion Problem

Journal of scientific computing, 2020, Vol.82 (1), p.10, Article 10

2020

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A general collocation analysis for weakly singular Volterra integral equations with variable exponent

IMA journal of numerical analysis, 2024-10, Vol.44 (5), p.2725-2751

2024

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Collocation Methods for General Caputo Two-Point Boundary Value Problems

Journal of scientific computing, 2018-07, Vol.76 (1), p.390-425

2018

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Optimal Long-Time Decay Rate of Numerical Solutions for Nonlinear Time-Fractional Evolutionary Equations

SIAM journal on numerical analysis, 2023-01, Vol.61 (5), p.2011-2034

2023

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Sharp Error Bounds for a Fractional Collocation Method for Weakly Singular Volterra Integral Equations with Variable Exponent

Journal of scientific computing, 2024-08, Vol.100 (2), p.41, Article 41

2024

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A discrete comparison principle for the time-fractional diffusion equation

Computers & mathematics with applications (1987), 2020-09, Vol.80 (5), p.917-922

2020

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A Posteriori Error Analysis for Variable-Coefficient Multiterm Time-Fractional Subdiffusion Equations

Journal of scientific computing, 2022-08, Vol.92 (2), p.73, Article 73

2022

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The local discontinuous Galerkin method for a singularly perturbed convection–diffusion problem with characteristic and exponential layers

Numerische Mathematik, 2023-06, Vol.154 (1-2), p.283-318

2023

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A sharp discrete convolution sum estimate

Communications in nonlinear science & numerical simulation, 2023-02, Vol.117, p.106923, Article 106923

2023

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Block boundary value methods for solving linear neutral Volterra integro-differential equations with weakly singular kernels

Journal of computational and applied mathematics, 2022-02, Vol.401, p.113747, Article 113747

2022

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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

Numerical algorithms, 2024-03, Vol.95 (3), p.1155-1176

2024

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A Survey of the L1 Scheme in the Discretisation of Time-Fractional Problems

ERROR ANALYSIS OF A FINITE DIFFERENCE METHOD ON GRADED MESHES FOR A TIME-FRACTIONAL DIFFUSION EQUATION

Sharp anisotropic interpolation error estimates for rectangular Raviart-Thomas elements

Steady-state convection-diffusion problems

Supercloseness of the local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem

An Alternative Finite Difference Stability Analysis for a Multiterm Time-Fractional Initial-Boundary Value Problem

Too Much Regularity May Force Too Much Uniqueness

Fractional-order derivatives defined by continuous kernels are too restrictive

Good (and Not So Good) Practices in Computational Methods for Fractional Calculus

Error Analysis of a Second-Order Method on Fitted Meshes for a Time-Fractional Diffusion Problem

Blow-up of error estimates in time-fractional initial-boundary value problems

Optimal spatial H 1 -norm analysis of a finite element method for a time-fractional diffusion equation

A Nyström method based on product integration for weakly singular Volterra integral equations with variable exponent

α-robust error analysis of a mixed finite element method for a time-fractional biharmonic equation

Superconvergence of a Finite Element Method for the Multi-term Time-Fractional Diffusion Problem

A general collocation analysis for weakly singular Volterra integral equations with variable exponent

Collocation Methods for General Caputo Two-Point Boundary Value Problems

Optimal Long-Time Decay Rate of Numerical Solutions for Nonlinear Time-Fractional Evolutionary Equations

Sharp Error Bounds for a Fractional Collocation Method for Weakly Singular Volterra Integral Equations with Variable Exponent

A discrete comparison principle for the time-fractional diffusion equation

A Posteriori Error Analysis for Variable-Coefficient Multiterm Time-Fractional Subdiffusion Equations

The local discontinuous Galerkin method for a singularly perturbed convection–diffusion problem with characteristic and exponential layers

A sharp discrete convolution sum estimate

Block boundary value methods for solving linear neutral Volterra integro-differential equations with weakly singular kernels

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

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