# 12月28日　上海师范大学田红炯教授学术报告

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.