主講人：廖洪林 南京航空航天大學(xué)教授

時(shí)間：2022年10月21日14：00

地點(diǎn)：騰訊會(huì)議 238 595 317

舉辦單位：數(shù)理學(xué)院

主講人介紹：廖洪林，應(yīng)用數(shù)學(xué)博士，2018年至今任教于南京航空航天大學(xué)數(shù)學(xué)學(xué)院。2001年在解放軍理工大學(xué)獲理學(xué)碩士學(xué)位，2010年在東南大學(xué)獲理學(xué)博士學(xué)位，2001-2017年任教于解放軍理工大學(xué)。學(xué)術(shù)研究方向?yàn)槠⒎址e分方程數(shù)值解，目前主要關(guān)注相場(chǎng)以及多相流模型的時(shí)間變步長(zhǎng)離散與自適應(yīng)算法, 在Math Comp，SIAM J Numer Anal, SIAM J Sci Comput，IMA J Numer Anal，J Comput Phys, Sci China Math等國(guó)內(nèi)外專(zhuān)業(yè)期刊上發(fā)表學(xué)術(shù)研究論文三十余篇。

內(nèi)容介紹：The discrete gradient structure and the positive definiteness of discrete fractional integrals or derivatives are fundamental to the numerical stability in long-time simulation of nonlinear integro-differential models. We bulid up a discrete gradient structure for a class of second-order variable-step approximations of fractional Riemann-Liouville integral and fractional Caputo derivative. Then certain variational energy dissipation laws at discrete levels of the corresponding variable-step Crank-Nicolson type methods are established for time-fractional Allen-Cahn and time-fractional Klein-Gordon type models. They are shown to be asymptotically compatible with the associated energy law of the classical Allen-Cahn and Klein-Gordon equations in the associated fractional order limits. Numerical examples together with an adaptive time-stepping procedure are provided to demonstrate the effectiveness of our second-order methods.