讲座主题：A novel high-order time-stepping approach for gradient flow models based on the Taylor series methods

专家姓名：齐龙昭

工作单位：河北师范大学数学科学学院

讲座时间：2024年12月07日11:00-12:00

讲座地点：数学院大会议室341

主办单位：欧宝官方app下载数学与信息科学学院

内容摘要：

In this talk, we develop a high-order time-stepping technique for gradient flow models. The method is based on linear energy-stable convex splitting scheme and high-order accuracy is achieved by using the Taylor series technique. This method only requires solving a sequence of linear equations with constant coefficient at each time step and the nonlinear terms are explicitly updated in this framework, so it is very efficient and easy to implement. The proposed technique allows one to design schemes of any order in time using only two time levels. To the best of our knowledge, this is the first attempt to construct high-order linear numerical schemes based on the Taylor series method for solving gradient flow models. It also provides a new perspective for constructing high-order numerical schemes for other dissipative systems. We also perform simulations for the phase transition behaviors to show the capability of the proposed method.

主讲人介绍：

齐龙昭，河北师范大学数学科学学院讲师，2022年12月博士毕业于西安交通大学，主要研究方向为流体力学和相场模型中的高效数值方法，现主持校级科研启动基金项目一项，在Journal of Scientific Computing、Journal of Computational and Applied Mathematics、Computers and Mathematics with Applications等国际知名SCI学术期刊上发表论文多篇。