What is he best known for?
The fields of study he is best known for:
- Mathematical analysis
- Partial differential equation
- Numerical analysis
Martin Stynes focuses on Mathematical analysis, Singular perturbation, Convection–diffusion equation, Finite difference method and Boundary value problem. In Mathematical analysis, Martin Stynes works on issues like Discontinuous Galerkin method, which are connected to Mixed finite element method. His studies deal with areas such as Elliptic curve and Reaction–diffusion system as well as Singular perturbation.
His Convection–diffusion equation research is multidisciplinary, incorporating perspectives in Numerical solution of the convection–diffusion equation, Differential operator and Unit square. He combines subjects such as Discretization, Fractional calculus, Numerical analysis and Boundary with his study of Finite difference method. In his research on the topic of Boundary value problem, Boundary layer, Interval and Scheme is strongly related with Upwind scheme.
His most cited work include:
- Numerical Methods for Singularly Perturbed Differential Equations (903 citations)
- Numerical methods for singularly perturbed differential equations : convection-diffusion and flow problems (422 citations)
- Robust Numerical Methods for Singularly Perturbed Differential Equations: Convection-Diffusion-Reaction and Flow Problems (287 citations)
What are the main themes of his work throughout his whole career to date?
Martin Stynes mainly focuses on Mathematical analysis, Boundary value problem, Numerical analysis, Convection–diffusion equation and Singular perturbation. His work in the fields of Mathematical analysis, such as Finite difference method, Norm, Piecewise and Differential equation, intersects with other areas such as Uniform convergence. His Boundary value problem research includes themes of Upwind scheme, Reaction–diffusion system, Fractional calculus, Applied mathematics and Boundary layer.
His Numerical analysis research is multidisciplinary, incorporating elements of Differential operator, Finite difference, Derivative, Discretization and Maximum principle. The study incorporates disciplines such as Unit square, Boundary, Galerkin method and Exponential function in addition to Convection–diffusion equation. His research investigates the connection with Singular perturbation and areas like Method of matched asymptotic expansions which intersect with concerns in Asymptotic expansion.
He most often published in these fields:
- Mathematical analysis (58.52%)
- Boundary value problem (34.66%)
- Numerical analysis (29.55%)
What were the highlights of his more recent work (between 2016-2021)?
- Applied mathematics (21.59%)
- Fractional calculus (15.34%)
- Boundary value problem (34.66%)
In recent papers he was focusing on the following fields of study:
The scientist’s investigation covers issues in Applied mathematics, Fractional calculus, Boundary value problem, Mathematical analysis and Singularity. He has included themes like Discretization, Superconvergence, Norm and Piecewise in his Applied mathematics study. The various areas that Martin Stynes examines in his Fractional calculus study include Zero, Integer, Numerical analysis and Bounded function.
His study in Boundary value problem is interdisciplinary in nature, drawing from both Volterra integral equation, Green's function, Collocation method and Discontinuous Galerkin method. He integrates several fields in his works, including Mathematical analysis and Multi dimensional. His Singularity research incorporates themes from Pointwise, Polygon mesh and Time derivative.
Between 2016 and 2021, his most popular works were:
- Error Analysis of a Finite Difference Method on Graded Meshes for a Time-Fractional Diffusion Equation (252 citations)
- Error Analysis of a Second-Order Method on Fitted Meshes for a Time-Fractional Diffusion Problem (33 citations)
- Analysis and numerical solution of a Riemann-Liouville fractional derivative two-point boundary value problem (30 citations)
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