报告主题：时间分数阶反应扩散方程解的正则性及其非均匀网格差分方法
报告人：Martin Stynes 教授 （北京计算科学研究中心）
报告时间：2017年 11月10日（周五）10:00
报告地点：校本部G507
邀请人：李常品
报告摘要：A reaction-diffusion initial-boundary problem with a Caputo time derivative of order $\alpha\in (0,1)$ is considered. The solution of such a problem is discussed at length; it is shown that in general the solution has a weak singularity at the initial time $t=0$, and sharp pointwise bounds on the derivatives of this solution are derived. These bounds are then used in a new analysis of a standard finite difference method for the problem. This analysis encompasses both uniform meshes and meshes that are graded in time, and includes new stability and consistency bounds. The final convergence result shows clearly how the regularity of the solution and the grading of the mesh affect the order of convergence of the difference scheme, so one can choose an optimal mesh grading to solve the problem numerically.
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