演讲人Speaker：廖洪林 教授

题目Title:Adaptive second-order time-stepping schemes for time fractional MBEmodels

时间Date：  2019 年 10 月 13 日      Time：10：30--11：30

地点Venue： T3 栋 605 室

内容摘要Abstract：

Adaptive second-order Crank-Nicolson time-stepping methods using the recentscalar auxiliary variable (SAV) approach are developed for thetime-fractional molecular beam epitaxial models.Based on the piecewise linear interpolation, the Caputo's fractionalderivative is approximated by a novel second-order formula, which isnaturally suitable for a general class of nonuniform meshes and essentiallypreserves the positive semi-definite property of integral kernel. Theresulting Crank-Nicolson SAVtime-stepping schemes are unconditional energystable on nonuniform time meshes, and are computationally efficient inmultiscale time simulations when combined with adaptive time steps, such asare appropriate for accurately resolving the intrinsically initialsingularity of solution and for efficiently capturing the fast dynamicsaway initial time. Numerical examples are presented to show theeffectiveness of our methods.

个人简介(About the speaker):

廖洪林，应用数学博士，现任教于南京航空航天大学数学系。2001年硕士毕业于解放军理工大学应用数学与物理系，2010年博士毕业于东南大学数学系。学术研究方向为偏微分方程数值解与数值并行算法，目前主要关注分数阶与非局部偏微分方程的非均匀离散逼近。在《SIAM Journal on Numerical Analysis》, 《SIAM Journal on Scientific Computing》,《Journal of Computational Physics》, 《Advance in Computational Mathematics》， 《Journal of Scientific Computing》, 《Numerical Algorithms》, 《中国科学》等国内外专业期刊上发表学术论文二十余篇，被引500余次。