報告人：鄧定文（南昌航空大學）

報告題目：Two structure-preserving finite difference methods for Fisher-Kolmogorov-Petrovsky-Piscounov equation and Allen-Cahn equation

報告摘要：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.

報告時間：2025年3月1日（星期六）8:00-10:00

報告地點：科技樓706會議室

邀請人：張誠堅

報告人簡介：鄧定文，博士，南昌航空大學教授，碩士生導師，主要從事偏微分方程數值解法研究；主持國家自然科學基金四項，主持包括中國博士後科學基金，江西省重點項目，江西省傑出青年基金在内的各類省 (部) 級和廳級科研項目 11 項；受國家留學基金委面上項目的資助于2016-12-01至 2017-11-30訪問加拿大約克大學88858cc永利；2015年入選南昌航空大學青年英才開發計劃，在國内外專業刊物上發表學術論文近 60篇。