报告人：闫玉斌 教授 吕梁学院（切斯特大学）
报告题目一：Two high-order time discretization schemes for subdiffusion problems with nonsmooth data
摘 要：Two new high-order time discretization schemes for solving subdiffusion problems with nonsmooth data are developed based on the corrections of the existing time discretization schemes in literature. Without the corrections, the schemes have only a first order of accuracy for both smooth and nonsmooth data. After correcting some starting steps and some weights of the schemes, the optimal convergence orders O(k3-α) and O(k4-α) with 0<α<1 can be restored for any fixed time for both smooth and nonsmooth data, respectively. The error estimates for these two new high-order schemes are proved by using Laplace transform method for both homogeneous and inhomogeneous problem. Numerical examples are given to show that the numerical results are consistent with the theoretical results.
报告题目二：On implicit time stepping methods for a time fractional cable equation with nonsmooth data
摘 要：In this paper, we introduce and analyze two time discretization schemes for approximating the time fractional cable equation. The time derivative is approximated by using the backward Euler method and the second order backward difference formula, and the Riemann-Liouville fractional derivatives are approximated by using the convolution quadratures generated by the backward Euler method and the second order backward difference formula, respectively. The nonsmooth data error estimates of the time discretization schemes with the convergence orders O(k) and O(k2) are proved. Instead of using the discretized operational calculus approach to analyze such time discretization schemes as in literature, we directly bound the approximation error of the kernel function to obtain nonsmooth data error estimates following the argument in Lubich et al. [ Math.Comp. 65 (1996), pp. 1-17]. This argument may be applied to analyze the nonsmooth data error estimates of other time discretization scheme for approximating the time fractional cable equation, where the Riemann-Liouville fractional derivatives are approximated by using, say for example, L1 scheme. Moreover, several generalizations expanding the scope of the proposed technique are also briefly reported. Finally, numerical experiments are conducted to confirm our theoretical findings.
报告人简介：闫玉斌教授目前是吕梁学院特聘教授、英国切斯特大学(University of Chetser)数学系终身教授。他于2003年在瑞典查尔莫斯工业大学(Chalmers University of Technology)获得数学博士学位。2003-2004在英国曼切斯特大学(University of Manchester)数学系从事博士后研究，2004-2007在英国谢菲尔德大学(University of Sheffield)自动控制和工程系从事博士后研究。2007-至今在英国切斯特大学(University of Chetser)数学系任教。主要从事分数阶微分方程的数值解，随机微分方程的数值解，有限差分，有限元方法的研究。应邀在各类国际学术会议上报告60多次。多次组织和主办分数阶问题的国际研讨班。已成功指导博士5位,先后邀请6位国内高校博士来英国切斯特大学(University of Chetse)从事6-12个月的博士后研究。担任Applied Numerical Mathematic, Fractional Calculus in Applied Analysis等多个国际期刊的编委和副主编。主持和参与英国EPSRC项目两项，国家自然科学基金一项。在SIAM J. Numerical Analysis, BIT, IMA J. Numerical Analysis等数值分析领域的顶级期刊上发表了80多篇SCI论文。论文他引1800多次(Google Scholar)。研究成果在随机抛物型方程和分数阶微分方程的数值分析研究领域有着广泛的影响，一些论文被同行认定为该研究领域的经典参考文献而被广泛引用。
报告时间：2024年7月20日，上午8：30-11：00
报告地点：明远楼410
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内蒙古大学数学科学学院
2024年7月15日
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