Martin Stynes

Numerical Analysis · 2001–2020

A researcher in the Science corpus: 13 papers; trusts 13 researchers and is trusted by 21 researchers here, as inferred from the citation graph.

Subfields

• Numerical Analysis — 37 citations into it; #844 of 3,586 by trust here, #583 by citations
• Modeling and Simulation — 35 citations into it; #369 of 2,105 by trust here, #628 by citations
• Applied Mathematics — 28 citations into it; #2,564 of 7,620 by trust here, #3,794 by citations
• Computational Theory and Mathematics — 8 citations into it; #8,157 of 12,182 by trust here, #6,798 by citations
• Mechanics of Materials — 6 citations into it; #3,090 of 6,291 by trust here, #4,102 by citations
• Mathematical Physics — 5 citations into it

Whom Martin Stynes trusts overall

Their strongest outbound trust, strongest first, inferred from their citations.

1. Yumin Lin
2. Chuanju Xu
3. Hermann Brunner
4. William McLean
5. Kai Diethelm
6. Kenichi Sakamoto
7. Torsten Linß
8. Yuri Luchko
9. Francesco Mainardi
10. X. Li

Who trusts Martin Stynes overall

1. Hong-lin Liao
2. Pin Lyu
3. Hans-Görg Roos
4. William McLean
5. Neville J. Ford
6. Yuxiang Liang
7. S. Bellew
8. Bangti Jin
9. Zhibo Wang
10. Jiwei Zhang

Papers from Martin Stynes's perspective

Ordered by how strongly the researchers Martin Stynes trusts endorse each paper. Same corpus, a different order for every researcher.

1. Theory and Applications of Fractional Differential Equations
2. Finite difference/spectral approximations for the time-fractional diffusion equation (Journal of Computational Physics)
3. Fractional Calculus: Integral and Differential Equations of Fractional Order
4. General fractional calculus (Basic Theory)
5. The Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type
6. Generalized mittag-leffler function and generalized fractional calculus operators
7. Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models
8. Existence and Uniqueness of the Weak Solution of the Space-Time Fractional Diffusion Equation and a Spectral Method Approximation
9. A practical guide to Prabhakar fractional calculus (Fractional Calculus and Applied Analysis)
10. Desiderata for Fractional Derivatives and Integrals (Mathematics)

Their papers

• Corner singularities and boundary layers in a simple convection–diffusion problem☆ (2005) — 92 citations
• Blow-up of error estimates in time-fractional initial-boundary value problems (2020) — 101 citations
• Why fractional derivatives with nonsingular kernels should not be used (2020) — 142 citations
• Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation (2017) — 784 citations
• Too much regularity may force too much uniqueness (2016) — 137 citations
• An efficient collocation method for a Caputo two-point boundary value problem (2015) — 52 citations
• A two-scale sparse grid method for a singularly perturbed reaction-diffusion problem in two dimensions (2009) — 60 citations
• Using rectangular Qp elements in the SDFEM for a convection--diffusion problem with a boundary layer (2008) — 49 citations
• Numerical Treatment of Partial Differential Equations (2007) — 407 citations
• Numerical analysis of a singularly perturbed nonlinear reaction-diffusion problem with multiple solutions (2004) — 47 citations
• Richardson extrapolation for a convection-diffusion problem using a Shishkin mesh (2003) — 66 citations
• A uniformly convergent numerical method for a coupled system of two singularly perturbed linear reaction–diffusion problems (2003) — 157 citations
• Asymptotic Analysis and Shishkin-Type Decomposition for an Elliptic Convection–Diffusion Problem (2001) — 156 citations