报告时间：2023年6月3日（星期六）

报告地点：扬州大学瘦西湖校区数学科学学院56号楼204报告厅

报告一：王雨顺教授（南京师范大学）8:30-10:30

题目：守恒系统投影积分算子的超收敛性

摘要：Projection method is applicable in many fields. It is a natural and practical approach to construct invariant-preserving schemes for conservative systems by projecting the solution of any underlying numerical scheme onto the manifold determined by the invariant, and this process will be referred as projection integrator in the following. A general result for this integrator is that it can achieve the same order as the underlying method. In this talk, we propose a new projection integrator with superconvergence and further discover that the superconvergence is attributed to the projection direction. This talk also summarizes arbitrarily high-order projection integrators with superconvergence and rigorously proves truncation error by utilizing the linear integral methods as a central tool. Meanwhile, symmetry is a significant geometric property in the geometric integration for reversible differential equation, so we also establish arbitrarily high-order symmetric projection integrators with superconvergence. A thorough comparison with the standard projection integrator is carried out.

报告二：陈景润教授（中国科学技术大学）10:30-12:30

题目: 微分方程数值解：从传统方法到机器学习方法，再到随机特征方法

摘要：如何数值求解偏微分方程是科学与工程领域的重要问题。传统方法包括有限差分、有限元等。近年来深度学习也被利用来求解偏微分方程。本报告将从精度和效率两个方面，系统比较传统方法和机器学习方法的优缺点，并介绍最近发展的随机特征方法。

报告三：黄健飞教授（扬州大学）14:00-16:00

题目: EM Methods for Stochastic Caputo Fractional Differential Equations

摘要：EM methods are presented for numerically solving some kinds of stochastic fractional differential equations with initial value conditions. The problems involve constant-order Caputo derivative and variable-order Riemann-Liouville integral. For the presented EM methods, their strong convergence and the fast implementation are strictly analyzed, respectively. The interesting strong convergence rate, which depends on the value of fractional index, is obtained. Some numerical examples are provided to support our theoretical findings. And it is demonstrated that the computational performance of the fast EM method has the overwhelming advantage over the direct EM method.

主办单位：扬州大学数学科学学院

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