报 告 人： 田红炯 教授（上海师范大学）
报告题目：Asymptotic-numerical solvers for highly oscillatory second-order differential equations
报告时间：2019年12月28日（周六）上午9：00
报告地点：静远楼204报告厅
报告摘要：
In this talk, we propose an approach of combination of asymptotic and numerical techniques to solve highly oscillatory second-order initial value problems. An asymptotic expansion of the solution is derived in inverse of powers of the oscillatory parameter, which develops on two time scales, a slow time $t$ and a fast time $\tau=\omega t$. The truncation with the first few terms of the expansion results in a very effective method of discretizing the highly oscillatory differential equation and becomes more accurate when the oscillatory parameter increases. Numerical examples show that our proposed asymptotic-numerical solver is efficient and accurate for highly oscillatory problems.