M. Stynes

activity

20192025

most citedWhy fractional derivatives with nonsingular kernels should not be used

155 citations · 156 across the 3 of their papers we have counts for

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math.NA2025

Uniform error analysis of a rectangular Morley finite element method on a Shishkin mesh for a 4th-order singularly perturbed boundary value problem

Xiangyun Meng, Martin Stynes

The singularly perturbed reaction-diffusion problem $ε^{2} Δ^{2} u - div (c \nabla u) = f$ is considered on the unit square $Ω$ in $R^{2}$ with homoge…

math.NA2022★ 1 cited

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

Yao Cheng, Martin Stynes

A singularly perturbed convection-diffusion problem,posed on the unit square in $R^{2}$ , is studied; its solution has both exponential and characteristic boundary layers. Th…

math.NA2022

Optimal long-time decay rate of solutions of complete monotonicity-preserving schemes for nonlinear time-fractional evolutionary equations

Dongling Wang, Martin Stynes

The solution of the nonlinear initial-value problem $D_{t}^{α} y (t) = - λ y (t)^{γ}$ for $t > 0$ with $y (0) > 0$ , where $D_{t}^{α}$ is a Caputo derivative of order $α \in (0, 1)$ …