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| 1 | A Parameter-Uniform Finite Difference Method for a Coupled System of Convection-Diffusion Two-Point Boundary Value Problems显示文摘A system of m (≥2) linear convection-diffusion two-point boundary value problems is examined,where the diffusion term in each equation is multiplied by a small parameterεand the equations are coupled through their convective and reactive terms via matrices B and A respectively.This system is in general singularly perturbed. Unlike the case of a single equation,it does not satisfy a conventional maximum princi- ple.Certain hypotheses are placed on the coupling matrices B and A that ensure exis- tence and uniqueness of a solution to the system and also permit boundary layers in the components of this solution at only one endpoint of the domain;these hypotheses can be regarded as a strong form of diagonal dominance of B.This solution is decomposed into a sum of regular and layer components.Bounds are established on these compo- nents and their derivatives to show explicitly their dependence on the small parameterε.Finally,numerical methods consisting of upwinding on piecewise-uniform Shishkin meshes are proved to yield numerical solutions that are essentially first-order conver- gent,uniformly inε,to the true solution in the discrete maximum norm.Numerical results on Shishkin meshes are presented to support these theoretical bounds. | Eugene O'Riordan Jeanne Stynes Martin Stynes | 2008 | Numerical Mathematics(Theory,Methods and Applications)2008，1，2： | 3 |
| 2 | A Hybrid Difference Scheme on a Shishkin Mesh for Linear Convection-diffusion Problems 显示文摘 | Torsten Linb Martin Stynes | 1999 | Appl Numer Math1999，31，： | 1 |
| 3 | A robust adaptive method for a quasi-linear one dimensional convection-diffusion problem显示文摘 | NATALIA KOPTEVA MARTIN STYNES | 2001 | SIAM J Numer Anal2001，39，4： | 1 |
| 4 | The Midpoint Upwind Scheme显示文摘 | Martin Stynes | 1997 | Applied Numerical Mathematics1997，23，： | 1 |
| 5 | Richardson Extrapolation for a Convection-diffusion Problem Using a Shishkin Mesh显示文摘 | Mafia Caridad Natividad Martin Stynes | 2003 | Applied Numerical Mathematics2003，45，： | 1 |
| 6 | The streamline-diffusion method for nonconforming Qrot1 elements on rectangular tensor-product meshes显示文摘 | | 2001 | IMA Journal of Numerical Analysis2001，，21： | 1 |
| 7 | Richardson Extrapolation for a Convection-diffusion Problem Using a Shishkin Mesh显示文摘 | Maria Caridad Natividad Martin stynes | 2003 | Applied Numerical Mathematics2003，45，： | 1 |
| 8 | Asymptotic analysis and Shishkin-type decomposition for an elliptic convection-diffusion Problem 显示文摘 | Torsten Linfl Martin Stynes | 2001 | Journal of Mathematical Analysis and Applications2001，261，： | 1 |
| 9 | A Survey of the L1 Scheme in the Discretisation of Time-Fractional Problems显示文摘A survey is given of convergence results that have been proved when the L1 scheme is used to approximate the Caputo time derivative D_(t)^(α)(where 0<α<1)in initial-boundary value problems governed by D_(t)^(α)u−△u=f and similar equations,while taking into account the weak singularity that is present in typical solutions of such problems.Various aspects of these analyses are outlined,such as global and local convergence bounds and the techniques used to derive them,fast implementation of the L1 scheme,semilinear problems,multi-term time derivatives,α-robustness,a posteriori error analysis,and two modified L1 schemes that achieve better accuracy.Over fifty references are provided in the bibliography,more than half of which are from the period 2019-2022. | Martin Stynes | 2022 | Numerical Mathematics(Theory,Methods and Applications)2022，15，4： | 0 |
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