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2020 – today
- 2025
[j74]Zheng Ma, Martin Stynes
:
A Nyström method based on product integration for weakly singular Volterra integral equations with variable exponent. J. Comput. Appl. Math. 454: 116164 (2025)- 2024
- [j73]Minghua Chen, Weihua Deng, Chao Min, Jiankang Shi, Martin Stynes:
Error analysis of a collocation method on graded meshes for a fractional Laplacian problem. Adv. Comput. Math. 50(3): 49 (2024) - [j72]José Luis Gracia, Martin Stynes:
A collocation method for an RLC fractional derivative two-point boundary value problem with a singular solution. Comput. Appl. Math. 43(4): 199 (2024) - [j71]Yongtao Zhou, Hongyu Qin, Martin Stynes:
An α-robust error analysis of the L1‾ scheme for time-fractional integro-differential initial-boundary value problems. Comput. Math. Appl. 162: 196-205 (2024) - [j70]Zheng Ma, Martin Stynes:
Sharp Error Bounds for a Fractional Collocation Method for Weakly Singular Volterra Integral Equations with Variable Exponent. J. Sci. Comput. 100(2): 41 (2024) - [j69]Yao Cheng, Xuesong Wang, Martin Stynes:
Optimal Balanced-Norm Error Estimate of the LDG Method for Reaction-Diffusion Problems I: The One-Dimensional Case. J. Sci. Comput. 100(2): 50 (2024) - [j68]Yongtao Zhou, Cui Li, Martin Stynes:
A fast second-order predictor-corrector method for a nonlinear time-fractional Benjamin-Bona-Mahony-Burgers equation. Numer. Algorithms 95(2): 693-720 (2024) - [j67]Xiangyun Meng, Martin Stynes:
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 95(3): 1155-1176 (2024) - [i6]José Luis Gracia, Eugene O'Riordan, Martin Stynes:
A fitted scheme for a Caputo initial-boundary value problem. CoRR abs/2401.16156 (2024) - [i5]Yao Cheng, Xuesong Wang, Martin Stynes:
Optimal balanced-norm error estimate of the LDG method for reaction-diffusion problems II: the two-dimensional case with layer-upwind flux. CoRR abs/2405.11939 (2024) - 2023
- [j66]Martin Stynes, Dongling Wang:
A sharp discrete convolution sum estimate. Commun. Nonlinear Sci. Numer. Simul. 117: 106923 (2023) - [j65]Enyu Fan, Changpin Li, Martin Stynes:
Discretised general fractional derivative. Math. Comput. Simul. 208: 501-534 (2023) - [j64]Yao Cheng, Shan Jiang, Martin Stynes:
Supercloseness of the local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem. Math. Comput. 92(343): 2065-2095 (2023) - [j63]Yao Cheng, Martin Stynes:
The local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem with characteristic and exponential layers. Numerische Mathematik 154(1-2): 283-318 (2023) - [j62]Dongling Wang, Martin Stynes:
Optimal Long-Time Decay Rate of Numerical Solutions for Nonlinear Time-Fractional Evolutionary Equations. SIAM J. Numer. Anal. 61(5): 2011-2034 (2023) - 2022
- [j61]Hu Chen, Martin Stynes:
Using Complete Monotonicity to Deduce Local Error Estimates for Discretisations of a Multi-Term Time-Fractional Diffusion Equation. Comput. Methods Appl. Math. 22(1): 15-29 (2022) - [j60]Yongtao Zhou, Martin Stynes:
Block boundary value methods for solving linear neutral Volterra integro-differential equations with weakly singular kernels. J. Comput. Appl. Math. 401: 113747 (2022) - [j59]Chaobao Huang, Martin Stynes:
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. J. Sci. Comput. 91(2): 43 (2022) - [j58]Xiangyun Meng, Martin Stynes:
Balanced-Norm and Energy-Norm Error Analyses for a Backward Euler/FEM Solving a Singularly Perturbed Parabolic Reaction-Diffusion Problem. J. Sci. Comput. 92(2): 67 (2022) - [j57]Natalia Kopteva, Martin Stynes:
A Posteriori Error Analysis for Variable-Coefficient Multiterm Time-Fractional Subdiffusion Equations. J. Sci. Comput. 92(2): 73 (2022) - [i4]Natalia Kopteva, Martin Stynes:
A posteriori error analysis for variable-coefficient multiterm time-fractional subdiffusion equations. CoRR abs/2202.13357 (2022) - [i3]Dongling Wang, Martin Stynes:
Optimal long-time decay rate of solutions of complete monotonicity-preserving schemes for nonlinear time-fractional evolutionary equations. CoRR abs/2204.04673 (2022) - [i2]Yao Cheng, Shan Jiang, Martin Stynes:
Supercloseness of the local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem. CoRR abs/2206.08642 (2022) - [i1]Yao Cheng, Martin Stynes:
The local discontinuous Galerkin method for a singularly perturbed convection-diffusion problem with characteristic and exponential layers. CoRR abs/2209.10143 (2022) - 2021
- [j56]Lin Wang, Martin Stynes:
An α-robust finite difference method for a time-fractional radially symmetric diffusion problem. Comput. Math. Appl. 97: 386-393 (2021) - [j55]Jinye Shen, Martin Stynes, Zhi-Zhong Sun:
Two Finite Difference Schemes for Multi-Dimensional Fractional Wave Equations with Weakly Singular Solutions. Comput. Methods Appl. Math. 21(4): 913-928 (2021) - [j54]José Luis Gracia, Martin Stynes:
A finite difference method for an initial-boundary value problem with a Riemann-Liouville-Caputo spatial fractional derivative. J. Comput. Appl. Math. 381: 113020 (2021) - [j53]Chaobao Huang, Martin Stynes, Hu Chen:
An α-robust finite element method for a multi-term time-fractional diffusion problem. J. Comput. Appl. Math. 389: 113334 (2021) - [j52]Kim-Ngan Le, Martin Stynes:
An α-Robust Semidiscrete Finite Element Method for a Fokker-Planck Initial-Boundary Value Problem with Variable-Order Fractional Time Derivative. J. Sci. Comput. 86(2): 22 (2021) - [j51]Chaobao Huang, Martin Stynes:
α-robust error analysis of a mixed finite element method for a time-fractional biharmonic equation. Numer. Algorithms 87(4): 1749-1766 (2021) - 2020
- [j50]Chaobao Huang, Martin Stynes:
Optimal H1 spatial convergence of a fully discrete finite element method for the time-fractional Allen-Cahn equation. Adv. Comput. Math. 46(4): 63 (2020) - [j49]Chaobao Huang, Martin Stynes:
Error analysis of a finite element method with GMMP temporal discretisation for a time-fractional diffusion equation. Comput. Math. Appl. 79(9): 2784-2794 (2020) - [j48]Hu Chen, Martin Stynes:
A discrete comparison principle for the time-fractional diffusion equation. Comput. Math. Appl. 80(5): 917-922 (2020) - [j47]Chaobao Huang, Xiaohui Liu, Xiangyun Meng, Martin Stynes:
Error Analysis of a Finite Difference Method on Graded Meshes for a Multiterm Time-Fractional Initial-Boundary Value Problem. Comput. Methods Appl. Math. 20(4): 815-825 (2020) - [j46]Chaobao Huang, Martin Stynes:
Optimal spatial H1-norm analysis of a finite element method for a time-fractional diffusion equation. J. Comput. Appl. Math. 367 (2020) - [j45]Chaobao Huang, Martin Stynes:
Superconvergence of a Finite Element Method for the Multi-term Time-Fractional Diffusion Problem. J. Sci. Comput. 82(1): 10 (2020) - [j44]Xiangyun Meng, Martin Stynes:
Barrier Function Local and Global Analysis of an L1 Finite Element Method for a Multiterm Time-Fractional Initial-Boundary Value Problem. J. Sci. Comput. 84(1): 5 (2020) - [j43]Guanglong Ma, Martin Stynes:
A direct discontinuous Galerkin finite element method for convection-dominated two-point boundary value problems. Numer. Algorithms 83(2): 741-765 (2020)
2010 – 2019
- 2019
- [j42]Hui Liang, Martin Stynes:
Collocation methods for general Riemann-Liouville two-point boundary value problems. Adv. Comput. Math. 45(2): 897-928 (2019) - [j41]Xiangyun Meng, Martin Stynes:
Convergence analysis of the Adini element on a Shishkin mesh for a singularly perturbed fourth-order problem in two dimensions. Adv. Comput. Math. 45(2): 1105-1128 (2019) - [j40]Stephen Russell, Martin Stynes:
Balanced-norm error estimates for sparse grid finite element methods applied to singularly perturbed reaction-diffusion problems. J. Num. Math. 27(1): 37-55 (2019) - [j39]Hu Chen, Martin Stynes:
Error Analysis of a Second-Order Method on Fitted Meshes for a Time-Fractional Diffusion Problem. J. Sci. Comput. 79(1): 624-647 (2019) - 2018
- [j38]Martin Stynes:
Fractional-order derivatives defined by continuous kernels are too restrictive. Appl. Math. Lett. 85: 22-26 (2018) - [j37]José Luis Gracia, Eugene O'Riordan, Martin Stynes:
Convergence in Positive Time for a Finite Difference Method Applied to a Fractional Convection-Diffusion Problem. Comput. Methods Appl. Math. 18(1): 33-42 (2018) - [j36]Thái Anh Nhan, Martin Stynes, Relja Vulanovic:
Optimal uniform-convergence results for convection-diffusion problems in one dimension using preconditioning. J. Comput. Appl. Math. 338: 227-238 (2018) - [j35]Hui Liang, Martin Stynes:
Collocation Methods for General Caputo Two-Point Boundary Value Problems. J. Sci. Comput. 76(1): 390-425 (2018) - [j34]Jose L. Gracia, Eugene O'Riordan, Martin Stynes:
A Fitted Scheme for a Caputo Initial-Boundary Value Problem. J. Sci. Comput. 76(1): 583-609 (2018) - [c3]Hu Chen, Martin Stynes:
A High Order Method on Graded Meshes for a Time-Fractional Diffusion Problem. FDM 2018: 15-27 - 2017
- [j33]Natalia Kopteva, Martin Stynes:
Analysis and numerical solution of a Riemann-Liouville fractional derivative two-point boundary value problem. Adv. Comput. Math. 43(1): 77-99 (2017) - [j32]Martin Stynes, José Luis Gracia:
Preprocessing schemes for fractional-derivative problems to improve their convergence rates. Appl. Math. Lett. 74: 187-192 (2017) - [j31]Martin Stynes, Eugene O'Riordan, José Luis Gracia:
Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation. SIAM J. Numer. Anal. 55(2): 1057-1079 (2017) - 2016
- [j30]Can Huang, Martin Stynes:
A spectral collocation method for a weakly singular Volterra integral equation of the second kind. Adv. Comput. Math. 42(5): 1015-1030 (2016) - [c2]José Luis Gracia, Eugene O'Riordan, Martin Stynes:
Convergence Outside the Initial Layer for a Numerical Method for the Time-Fractional Heat Equation. NAA 2016: 82-94 - 2015
- [j29]Martin Stynes, José Luis Gracia:
Boundary Layers in a Two-Point Boundary Value Problem with a Caputo Fractional Derivative. Comput. Methods Appl. Math. 15(1): 79-95 (2015) - [j28]Hans-Görg Roos, Martin Stynes:
Some Open Questions in the Numerical Analysis of Singularly Perturbed Differential Equations. Comput. Methods Appl. Math. 15(4): 531-550 (2015) - [j27]Jose L. Gracia, Martin Stynes:
Central difference approximation of convection in Caputo fractional derivative two-point boundary value problems. J. Comput. Appl. Math. 273: 103-115 (2015) - [j26]Runchang Lin, Martin Stynes:
A balanced finite element method for a system of singularly perturbed reaction-diffusion two-point boundary value problems. Numer. Algorithms 70(4): 691-707 (2015) - 2014
- [j25]Martin Stynes:
Sharp anisotropic interpolation error estimates for rectangular Raviart-Thomas elements. Math. Comput. 83(290): 2675-2689 (2014) - 2012
- [j24]Sebastian Franz, R. Bruce Kellogg, Martin Stynes:
Galerkin and streamline diffusion finite element methods on a Shishkin mesh for a convection-diffusion problem with corner singularities. Math. Comput. 81(278): 661-685 (2012) - [j23]Runchang Lin, Martin Stynes:
A Balanced Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems. SIAM J. Numer. Anal. 50(5): 2729-2743 (2012) - 2011
- [j22]Carmelo Clavero, Jose L. Gracia, Martin Stynes:
A simpler analysis of a hybrid numerical method for time-dependent convection-diffusion problems. J. Comput. Appl. Math. 235(17): 5240-5248 (2011) - [j21]Natalia Kopteva, Martin Stynes:
Stabilised approximation of interior-layer solutions of a singularly perturbed semilinear reaction-diffusion problem. Numerische Mathematik 119(4): 787-810 (2011) - [j20]Fang Liu, Martin Stynes, Aihui Zhou:
Postprocessed Two-Scale Finite Element Discretizations, Part I. SIAM J. Numer. Anal. 49(5): 1947-1971 (2011)
2000 – 2009
- 2009
- [j19]Eugene O'Riordan, Martin Stynes:
Numerical analysis of a strongly coupled system of two singularly perturbed convection-diffusion problems. Adv. Comput. Math. 30(2): 101-121 (2009) - [j18]Torsten Linß, Martin Stynes:
Numerical Solution of Systems of Singularly Perturbed Differential Equations. Comput. Methods Appl. Math. 9(2): 165-191 (2009) - [j17]Aidan Naughton, Martin Stynes:
Singularly Perturbed Convection - Diffusion Problems in One Dimension: Bounds on Derivatives. Comput. Methods Appl. Math. 9(3): 281-291 (2009) - 2008
- [j16]R. Bruce Kellogg, Torsten Linß, Martin Stynes:
A finite difference method on layer-adapted meshes for an elliptic reaction-diffusion system in two dimensions. Math. Comput. 77(264): 2085-2096 (2008) - [c1]Eugene O'Riordan, Jeanne Stynes, Martin Stynes:
An Iterative Numerical Algorithm for a Strongly Coupled System of Singularly Perturbed Convection-Diffusion Problems. NAA 2008: 104-115 - 2007
- [j15]R. Bruce Kellogg, Martin Stynes:
Sharpened bounds for corner singularities and boundary layers in a simple convection-diffusion problem. Appl. Math. Lett. 20(5): 539-544 (2007) - [j14]Martin Stynes:
Convection-diffusion-reaction problems, SDFEM/SUPG and a priori meshes. Int. J. Comput. Sci. Math. 1(2/3/4): 412-431 (2007) - 2006
- [j13]Martin Stynes, Natalia Kopteva:
Numerical analysis of singularly perturbed nonlinear reaction-diffusion problems with multiple solutions. Comput. Math. Appl. 51(5): 857-864 (2006) - 2005
- [j12]Natalia Kopteva, Niall Madden, Martin Stynes:
Grid equidistribution for reaction-diffusion problems in one dimension. Numer. Algorithms 40(3): 305-322 (2005) - 2003
- [j11]Martin Stynes, Lutz Tobiska:
The SDFEM for a Convection-Diffusion Problem with a Boundary Layer: Optimal Error Analysis and Enhancement of Accuracy. SIAM J. Numer. Anal. 41(5): 1620-1642 (2003) - 2001
- [j10]Martin Stynes, Lutz Tobiska:
Analysis of the streamline-diffusion finite element method on a piecewise uniform mesh for a convection-diffusion problem with exponential layers. J. Num. Math. 9(1): 59-76 (2001) - [j9]Torsten Linß, Martin Stynes:
The sdfem on Shishkin meshes for linear convection-diffusion problems. Numerische Mathematik 87(3): 457-484 (2001) - [j8]R. Bruce Kellogg, Martin Stynes:
n-Widths and Singularly Perturbed Boundary Value Problems II. SIAM J. Numer. Anal. 39(2): 690-707 (2001) - [j7]Natalia Kopteva, Martin Stynes:
A Robust Adaptive Method for a Quasi-Linear One-Dimensional Convection-Diffusion Problem. SIAM J. Numer. Anal. 39(4): 1446-1467 (2001)
1990 – 1999
- 1998
- [j6]Martin Stynes, Lutz Tobiska:
A finite difference analysis of a streamline diffusion method on a Shishkin mesh. Numer. Algorithms 18(3-4): 337-360 (1998) - 1997
- [j5]Wen Guo, Martin Stynes:
An analysis of a cell-vertex finite volume method for a parabolic convection-diffusion problem. Math. Comput. 66(217): 105-124 (1997) - [j4]K. W. Morton, Martin Stynes, Endre Süli:
Analysis of a cell-vertex finite volume method for convection-diffusion problems. Math. Comput. 66(220): 1389-1406 (1997) - 1996
- [j3]Guangfu Sun, Martin Stynes:
A uniformly convergent method for a singularly perturbed semilinear reaction-diffusion problem with multiple solutions. Math. Comput. 65(215): 1085-1109 (1996) - 1995
- [j2]Dirk Adam, Andreas Felgenhauer, Hans-Görg Roos, Martin Stynes:
A Nonconforming Finite Element Method for a Singularly Petrurbed Boundary Value Problem. Computing 54(1): 1-26 (1995) - 1994
- [j1]Guangfu Sun, Martin Stynes:
Finite element methods on piecewise equidistant meshes for interior turning point problems. Numer. Algorithms 8(1): 111-129 (1994)
Coauthor Index
Jose L. Gracia
aka: José Luis Gracia
aka: José Luis Gracia
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