2017年理学院数学学术交流系列报告（一）.doc

2017年理学院数学学术交流系列报告主题：报告地点：教楼 B109(理学院报告厅)报告时间：20175月9日下午2：30 报告: 盛秦教授（美国） 题：(Exponential Splitting and Their Applications for the Numerical Solution of Singular Reaction-Diffusion Equations) 摘要: This talk consists of two interactive components. First, we will pay an attention to existing splitting methods, such as the non-exponential ADI and exponential LOD methods, and explore their modernizations. Then we will focus at interesting issues involving the design and analysis of highly-effective and highly-efficient finite difference methods for solving singular reaction-diffusion equations which are important to various scientific applications including biology and bio-medicine. We will outline the physical background of the quenching phenomena related. Basic adaptive finite difference approaches will be introduced. Numerical analysis on their monotonicity, convergence and stability will be discussed. We will also discuss the latest exponential evolving grid development inspired by moving grid strategies. The general idea of such adaptations can be extended for solving similar multiphysics equations emerging from studies of biophysics, oil pipeline decay detection and laser-materials interactions. Certain stochastic inferences will be involved. 报告人：教授（大学） 题：阶扩（Finite Difference Methods for Fractional ）报阶导阶阶导带边阶扩阶带边阶扩阶带边阶扩 报告3：题： 报告人4：吴新元教授（南京大学） 题变应 摘要: This talk presents an operator-variation-of-constants formula withapplications for higher-dimensional nonlinear wave equations. When the operator is replaced by a differential matrix, the formula reduces to the so-called matrix-variation-of-constants formula, which has motivated the formulation of multi-frequency and multi-dimensional adapted Runge-Kutta-Nystr\{o}m (ARKN) methods, and multi-frequency and multi-dimensional extended Runge-Kutta-Nystr\{o}m (ERKN) integrators, or the generalized Gaustchi--type methods, for multi-frequency oscillatory differential equations. This talk also concerns AAVF methods,