应东北大学秦皇岛分校数学与统计学院张贵来的邀请，哈尔滨工业大学数学学院副教授杨占文，博士姚子晨，硕士李梦娜于2023年5月19日-2023年5月26日来我校访问，并进行了深入的交流。于5月20日上午9：00-11：00，在科技楼5075，姚子晨博士和李梦娜都作了精彩的学术报告。

报告题目：Analytical and numerical stability for fractional delay diffusion-wave equations.

报告人：姚子晨

摘要：This talk is mainly devoted to the analytical and numerical stability of fractional delay diffusion wave equations. Through a detailed analysis of the characteristic equations obtained by the Laplace transform, we introduce a novel integral path to deal with the awful singularities caused by delay and fractional exponent. We show that the longtime decay rate of the analytical solutions is O(t^(1\alpha)). Moreover, we also consider the stability of numerical solutions by fractional linear multistep methods in time and Galerkin finite element method in space. By virtue of the Z transform method, we obtain some numerical stability results. Finally, a numerical example is provided to show the effectiveness of our results.

报告题目：Numerical Threshold Dynamics for Age-structured Models by Higher order Collocation Methods

报告人：李梦娜

摘要：In this meeting, we mainly talk about numerical threshold dynamics for age-structured models by higher-order collocation methods.Firstly, we review some classic age-structured model, such as agestructured population model, SIR and HIV model. Secondly, we proposed an age-semi-discrete scheme by continuous collocation methods. And for the Lotka Mckendrick model with finite fertilityspan population, the numerical basic reproduction number Rh is provided. With the study of higherorder convergence to the real basic reproduction number R0, some conditions are also presented such that Rh is the threshold for numerical dynamical system of the age-semidiscretization.Thirdly, an equivalent block Leslie matrix expression is obtained by embedding into a piecewise discontinuous polynomial space rather than the piecewise-continuous polynomial space. An implicit full discrete scheme is considered with an explicit numerical birth, of which the computational cost is almost same as an explicit scheme. It is more important that the dynamical behavior of the age-semidiscretization system also is preserved for any time step whenever Rh is the threshold for numerical dynamical system of the agesemidiscretization. Finally, we show some numerical applications to population and COVID-19 models are shown to illustrate our results.