講座主題：A novel high-order time-stepping approach for gradient flow models based on the Taylor series methods
專家姓名：齊龍昭
工作單位：河北師范大學(xué)數(shù)學(xué)科學(xué)學(xué)院
講座時(shí)間：2024年12月07日11:00-12:00
講座地點(diǎn)：數(shù)學(xué)院大會(huì)議室341
主辦單位：煙臺(tái)大學(xué)數(shù)學(xué)與信息科學(xué)學(xué)院
內(nèi)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.
主講人介紹：
齊龍昭，河北師范大學(xué)數(shù)學(xué)科學(xué)學(xué)院講師，2022年12月博士畢業(yè)于西安交通大學(xué)，主要研究方向?yàn)榱黧w力學(xué)和相場(chǎng)模型中的高效數(shù)值方法，現(xiàn)主持校級(jí)科研啟動(dòng)基金項(xiàng)目一項(xiàng)，在Journal of Scientific Computing、Journal of Computational and Applied Mathematics、Computers and Mathematics with Applications等國(guó)際知名SCI學(xué)術(shù)期刊上發(fā)表論文多篇。
