报告人：盛秦
报告时间：年5月16日（星期三）14: 30-16:00
报告地点：宁夏大学怀远校区宁远楼（原数学楼）413会议室
报告题目：Notes on Derivative Approximations over Nonuiform Grids and Adaptive Numerical Solutions of Differential Equations
报告人简介：
盛秦(Sheng Qin)，英国剑桥大学获得数学博士学位，现为美国Baylor大学数学系终身教授，国际计算机数学杂志《International Journal of Computer Mathematics》主编。主要从事应用和计算数学研究，具体的研究方向包括：偏微分方程数值解法、算子分裂及区域分解法、自适应方法、高频振荡问题的数值分析、逼近论及方法、矩阵分析、计算金融、多物理场应用、并行计算、以工程应用为目标的软件设计等。出版学术专著6部，发表学术论文100余篇。
报告摘要：
Finite differences have been widely used in mathematical theory as well as scientic and engineering computations. Many difference formulas provide excellent approximations to different derivative functions, especially those used in modeling important physical processes, on uniform grids. However, it has been revealed that classical difference approximations on uniform grids cannot be extended blindly on nonuniform grids for approximating higher derivatives. At best, they may lose accuracy; at worst they are inconsistent.
Based on the study, we introduce nonuniform finite difference approximations for solving nonlinear partial differential equations adaptively. Several different designs of the monitoring function that targets anticipated quenching-type and degeneracy singularities are discussed following the equidistribution principle. The constructive approaches have been proven to be extremely effective and easy-to-use in multiphysical computations. The notes are due to recent collaborative work with A. D. Sheng, B. Jain and J. L. Padgett.
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宁夏大学数学统计学院
2018年5月13日
