题目： Sharp H^1-norm error estimates of two time-stepping schemes for reaction-subdiffusion problems
摘要： Due to the intrinsically initial singularity of solution and the discrete convolution form in numerical Caputo derivatives, the traditional H^1-norm analysis (corresponding to the case for a classical diffusion equation) to the time approximations of a fractional subdiffusion problem always leads to suboptimal error estimates (a loss of time accuracy). To recover the theoretical accuracy in time, we propose an improved discrete Gronwall inequality and apply it to the well-known L1 formula and a fractional Crank-Nicolson scheme. With the help of a time-space error-splitting technique and the global consistency analysis, sharp H^1-norm error estimates of the two nonuniform approaches are established for a reaction-subdiffusion problems. Numerical experiments are included to confirm the sharpness of our analysis.
报告人简介： 任金城，男，副教授，河南南阳人，河南财经政法大学永利体育官网登录工作。先后被评为河南省优秀教师，河南省高校科技创新人才、河南省教育厅学术技术带头人，河南财经政法大学青年拔尖人才等称号。现主要从事分数阶偏微分方程的数值算法研究, 主持国家自然科学基金项目2项，省高校科技创新人才项目1项，省厅级项目6项，获得省厅级奖励8项。在国际SCI期刊Journal of Computational Physics和Journal of Scientific Computing等杂志发表论文二十余篇。
时 间：2018-12-3日上午10:00-10:50。
地 点：永利体育官网登录3401教室。
报告对象：理工科专业本科生和研究生，各专业教师。
