Martin Stynes

9.1k total citations · 3 hit papers
187 papers, 6.9k citations indexed

About

Martin Stynes is a scholar working on Numerical Analysis, Computational Theory and Mathematics and Computational Mechanics. According to data from OpenAlex, Martin Stynes has authored 187 papers receiving a total of 6.9k indexed citations (citations by other indexed papers that have themselves been cited), including 162 papers in Numerical Analysis, 72 papers in Computational Theory and Mathematics and 68 papers in Computational Mechanics. Recurrent topics in Martin Stynes's work include Differential Equations and Numerical Methods (153 papers), Advanced Mathematical Modeling in Engineering (68 papers) and Advanced Numerical Methods in Computational Mathematics (64 papers). Martin Stynes is often cited by papers focused on Differential Equations and Numerical Methods (153 papers), Advanced Mathematical Modeling in Engineering (68 papers) and Advanced Numerical Methods in Computational Mathematics (64 papers). Martin Stynes collaborates with scholars based in Ireland, China and Germany. Martin Stynes's co-authors include Hans‐Görg Roos, Lutz Tobiska, Eugene O’Riordan, J.L. Gracia, Natalia Kopteva, Hu Chen, Chaobao Huang, Torsten Linß, R. Bruce Kellogg and Christian Großmann and has published in prestigious journals such as SHILAP Revista de lepidopterología, Journal of Computational Physics and Computer Methods in Applied Mechanics and Engineering.

In The Last Decade

Martin Stynes

181 papers receiving 6.5k citations

Hit Papers

align trajectories

What are hit papers?

Hit papers significantly outperform the citation benchmark for their cohort. A paper qualifies if it has ≥500 total citations, achieves ≥1.5× the top-1% citation threshold for papers in the same subfield and year (this is the minimum needed to enter the top 1%, not the average within it), or reaches the top citation threshold in at least one of its specific research topics.

Numerical Methods for Singularly Perturbed Differential Equations

1996 866 citations Hans‐Görg Roos, Martin Stynes et al. profile →
Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation

2017 686 citations Martin Stynes, Eugene O’Riordan et al. profile →
Robust Numerical Methods for Singularly Perturbed Differential Equations

2008 338 citations Hans‐Görg Roos, Martin Stynes et al. profile →

Peers — A (Enhanced Table)

Peers by citation overlap · career bar shows stage (early→late) cites · hero ref

Name	h						Papers	Cites
Martin Stynes Ireland	40	5.7k	2.9k	2.8k	2.0k	1.1k	187	6.9k
Yinnian He China	38	1.9k 0.3×	4.5k 1.6×	1.3k 0.5×	562 0.3×	391 0.4×	237	5.4k
Weiwei Sun China	32	1.5k 0.3×	1.7k 0.6×	678 0.2×	631 0.3×	385 0.3×	176	3.9k
Graeme Fairweather United States	36	1.5k 0.3×	1.5k 0.5×	629 0.2×	752 0.4×	294 0.3×	126	4.2k
R. Bruce Kellogg United States	27	1.6k 0.3×	1.5k 0.5×	1.4k 0.5×	144 0.1×	503 0.5×	93	3.2k
Zhi‐zhong Sun China	42	5.3k 0.9×	572 0.2×	265 0.1×	5.4k 2.7×	1.1k 1.0×	138	6.8k
Stefan Vandewalle Belgium	30	1.1k 0.2×	925 0.3×	695 0.2×	381 0.2×	362 0.3×	126	2.8k
Higinio Ramos Spain	28	2.2k 0.4×	564 0.2×	683 0.2×	924 0.5×	301 0.3×	194	2.8k
Ricardo H. Nochetto United States	37	1.0k 0.2×	3.9k 1.4×	2.3k 0.8×	184 0.1×	381 0.3×	170	5.1k
Ishak Hashim Malaysia	59	3.1k 0.5×	4.5k 1.6×	203 0.1×	4.6k 2.3×	717 0.6×	475	11.9k
Hans‐Görg Roos Germany	21	2.5k 0.4×	1.8k 0.6×	1.7k 0.6×	77 0.0×	405 0.4×	61	3.2k

Countries citing papers authored by Martin Stynes

Since Specialization

Citations

This map shows the geographic impact of Martin Stynes's research. It shows the number of citations coming from papers published by authors working in each country. You can also color the map by specialization and compare the number of citations received by Martin Stynes with the expected number of citations based on a country's size and research output (numbers larger than one mean the country cites Martin Stynes more than expected).

Fields of papers citing papers by Martin Stynes

Since Specialization

Physical SciencesHealth SciencesLife SciencesSocial Sciences

This network shows the impact of papers produced by Martin Stynes. Nodes represent research fields, and links connect fields that are likely to share authors. Colored nodes show fields that tend to cite the papers produced by Martin Stynes. The network helps show where Martin Stynes may publish in the future.

Co-authorship network of co-authors of Martin Stynes

This figure shows the co-authorship network connecting the top 25 collaborators of Martin Stynes. A scholar is included among the top collaborators of Martin Stynes based on the total number of citations received by their joint publications. Widths of edges represent the number of papers authors have co-authored together. Node borders signify the number of papers an author published with Martin Stynes. Martin Stynes is excluded from the visualization to improve readability, since they are connected to all nodes in the network.

All Works

Sort: Min cites: Since: Top N: Style:

20 of 20 papers shown

Stynes, Martin, et al.. (2024). A Nyström method based on product integration for weakly singular Volterra integral equations with variable exponent. Journal of Computational and Applied Mathematics. 454. 116164–116164.

Zhou, Yongtao, et al.. (2024). An α-robust error analysis of the L1‾ scheme for time-fractional integro-differential initial-boundary value problems. Computers & Mathematics with Applications. 162. 196–205. 1 indexed citations

Stynes, Martin, et al.. (2024). Sharp Error Bounds for a Fractional Collocation Method for Weakly Singular Volterra Integral Equations with Variable Exponent. Journal of Scientific Computing. 100(2). 3 indexed citations

Diethelm, Kai, Roberto Garrappa, & Martin Stynes. (2020). Good (and Not So Good) Practices in Computational Methods for Fractional Calculus. Mathematics. 8(3). 324–324. 43 indexed citations

Stynes, Martin. (2016). A Caputo Two-Point Boundary Value Problem: Existence, Uniqueness and Regularity of a Solution. SHILAP Revista de lepidopterología. 23(3). 370–376. 4 indexed citations

Stynes, Martin. (2014). Sharp anisotropic interpolation error estimates for rectangular Raviart-Thomas elements. Mathematics of Computation. 83(290). 2675–2689. 3 indexed citations

Clavero, C., J.L. Gracia, & Martin Stynes. (2011). A simpler analysis of a hybrid numerical method for time-dependent convection–diffusion problems. Journal of Computational and Applied Mathematics. 235(17). 5240–5248. 24 indexed citations

Stynes, Martin, et al.. (2010). Regularity and Derivative Bounds for a Convection-Diﬀusion Problem with Neumann Boundary Conditions on Characteristic Boundaries. Zeitschrift für Analysis und ihre Anwendungen. 29(2). 163–181.

Kellogg, R. Bruce, et al.. (2009). Regularity and derivative bounds for a convection–diffusion problem with a Neumann outflow condition. Journal of Differential Equations. 247(9). 2495–2516. 2 indexed citations

10.

Stynes, Martin & Natalia Kopteva. (2006). Numerical analysis of singularly perturbed nonlinear reaction-diffusion problems with multiple solutions. Computers & Mathematics with Applications. 51(5). 857–864. 7 indexed citations

11.

Madden, Niall, Martin Stynes, & Gareth Thomas. (1998). On the Development of Complete Flow Models for Wave-Current Interactions. Coastal dynamics. 405–414. 1 indexed citations

12.

Stynes, Martin & Lutz Tobiska. (1997). Error estimates and numerical experiments for streamline-diffusion-type methods on arbitrary and Shishkin meshes. Centrum Wiskunde & Informatica (CWI), the national research institute for mathematics and computer science in the Netherlands. 10. 337–352. 2 indexed citations

13.

Stynes, Martin & Eugene O’Riordan. (1997). A Uniformly Convergent Galerkin Method on a Shishkin Mesh for a Convection-Diffusion Problem. Journal of Mathematical Analysis and Applications. 214(1). 36–54. 103 indexed citations

14.

Roos, Hans‐Görg, Martin Stynes, & Lutz Tobiska. (1996). Numerical methods for singularly perturbed differential equations : convection-diffusion and flow problems. Springer eBooks. 372 indexed citations

15.

Roos, Hans‐Görg & Martin Stynes. (1996). Necessary conditions for uniform convergence of finite difference schemes for convection-diffusion problems with exponential and parabolic layers. Applications of Mathematics. 41(4). 269–280. 1 indexed citations

16.

Stynes, Martin. (1995). Finite volume methods for convection-diffusion problems. Journal of Computational and Applied Mathematics. 63(1-3). 83–90. 23 indexed citations

17.

Stynes, Martin. (1980). On Faster Convergence of the Bisection Method for all Triangles. Mathematics of Computation. 35(152). 1195–1195. 3 indexed citations

18.

Stynes, Martin. (1980). On faster convergence of the bisection method for all triangles. Mathematics of Computation. 35(152). 1195–1201. 35 indexed citations

19.

Stynes, Martin. (1979). On Faster Convergence of the Bisection Method for Certain Triangles. Mathematics of Computation. 33(146). 717–717. 5 indexed citations

20.

Stynes, Martin. (1979). On faster convergence of the bisection method for certain triangles. Mathematics of Computation. 33(146). 717–721. 40 indexed citations

Rankless uses publication and citation data sourced from OpenAlex, an open and comprehensive bibliographic database. While OpenAlex provides broad and valuable coverage of the global research landscape, it—like all bibliographic datasets—has inherent limitations. These include incomplete records, variations in author disambiguation, differences in journal indexing, and delays in data updates. As a result, some metrics and network relationships displayed in Rankless may not fully capture the entirety of a scholar's output or impact.

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