报告人：邓定文（南昌航空大学）

报告题目：Two structure-preserving finite difference methods for Fisher-Kolmogorov-Petrovsky-Piscounov equation and Allen-Cahn equation

报告摘要：This report discusses the development and analyses of two claasses of structure-preserving finite difference methods (FDMs) for Fisher-Kolmogorov-Petrovsky-Piscounov (Fisher-KPP) equation and Allen-Canh equation. To begin with, a class of explicit structure-preserving Du Fort-Frankel-type FDMs are developed for Fisher-KPP equation. They inherit some properties of the continuous problems, such as non-negativity, maximum principle and monotonicity. Secondly, a class of stabilized, implicitly, non-negativity- and boundedness-preserving FDMs are derived for Fisher-KPP equation. Thirdly, as they are applied to solve Allen-Cahn equation, the obtained solutions can unconditionally inherit the maximum value principle and energy-dissipation property of the Allen-Cahn equations. Finally, numerical results confirm the correctness of theoretical findings and high efficiencies of the proposed algorithms.

报告时间：2025年3月1日（星期六）8:00-10:00

报告地点：科技楼706会议室

邀请人：张诚坚

报告人简介：邓定文，博士，南昌航空大学教授，硕士生导师，主要从事偏微分方程数值解法研究；主持国家自然科学基金四项，主持包括中国博士后科学基金，江西省重点项目，江西省杰出青年基金在内的各类省 (部) 级和厅级科研项目 11 项；受国家留学基金委面上项目的资助于2016-12-01至 2017-11-30访问加拿大约克大学数学与统计学院；2015年入选南昌航空大学青年英才开发计划，在国内外专业刊物上发表学术论文近 60篇。