Martin Stynes，教授，博士生导师。主要从事奇异摄动微分方程和分数阶微分方程数值解的研究。他是《计算数学进展》、《应用数学计算方法》、《分数微积分和应用分析》、《科学计算杂志》和《爱尔兰皇家科学院数学学报》的编委会成员。

Time-fractional initial-boundary value problems of the form $D_t^\alpha u-p \partial^2 u/\partial x^2 +cu=f$ are considered, where $D_t^\alpha u$ is  a Caputo fractional derivative of order $\alpha\in (0,1)$. As $\alpha\to 1^-$, we prove that the solution $u$ converges, uniformly on the space-time domain, to the solution of the classical parabolic initial-boundary value problem where $D_t^\alpha u$ is replaced by $\partial u/\partial t$. Nevertheless, most of the rigorous analyses of numerical methods for this time-fractional problem have error bounds that blow up as $\alpha\to 1^-$, as we demonstrate. We show that in some cases these analyses can be modified to obtain robust error bounds that do not blow up as $\alpha\to 1^-$.