报告题目:An analysis of the modified L1 scheme for the time-fractional partial differential equations with nonsmooth data
报告人:闫玉斌 教授 吕梁学院(切斯特大学)
摘 要:We consider error estimates for the modified L1 scheme for solving time fractional partial differential equation. Jin et al. (2016, An analysis of the L1 scheme for the subdiffusion equation with nonsmooth data, IMA J. of Numer. Anal., 36, 197-221) established an O(k) convergence rate for the L1 scheme for both smooth and nonsmooth initial data. We introduce a modified L1 scheme and prove that the convergence rate is O(k2-α),0<α<1 for both smooth and nonsmooth initial data. We first write the time-fractional partial differential equation as a Volterra integral equation which is then approximated by using the convolution quadratures with some special generating functions. The numerical schemes obtained in this way are equivalent to the standard L1 scheme and the modified L1 scheme, respectively. A Laplace transform method is used to prove the error estimates for the homogeneous time-fractional partial differential equation for both smooth and nonsmooth data. Numerical examples are given to show that the numerical results are consistent with the theoretical results.
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18日,上午8:30-10:00
报告地点:明远楼410
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