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【歐洲杯八強競猜大講堂】 劉利斌:Analysis of a finite difference scheme for a nonlinear Caputo fractional differential equation on an adaptive grid

發布日期:2021-05-12    作者:     來源:     點擊:

題目:Analysis of a finite difference scheme for a nonlinear Caputo fractional differential equation on an adaptive grid

報告人:劉利斌(博士、南寧師范大學副教授、碩士生導師)

時間:2021年5月12日(周三)16:00-17:00

地點:博奕南一樓會議室

報告人簡介:

liulibin,boshi,nanningshifandaxueshuxueyutongjixueyuanfujiaoshou,shuoshishengdaoshi,guangxigaodengxuexiaodierpiqianmingguganjiaoshi。zhuyaoyanjiuxingquweiweifenfangchengshuzhijie、fenshujieweifenfangchengshuzhijiejizhinengsuanfajiqiyingyong。zhuchiwanchengguojiazirankexuejijin3xiang,guangxizirankexuejijin2xiang,anhuishenggaodengxuexiaoyouxiuqingnianrencaijijinzhongdianxiangmu1xiang。qijinweizhi,zaiguoneiwaigaoshuipingqikanshangfabiaoscilunwenjin40pian。

內容提要A nonlinear initial value problem whose the differential operator is a Caputo derivative of order $\alpha$ with $0<\alpha<1$ is studied. By using the Riemann-Liouville fractional integral transformation, this problem is reformulated as a Volterra integral equation, which is discretized by the right rectangle formula. Both an a priori and an a posteriori error analysis are conducted. Based on the a priori error bound and mesh equidistribution principle, we show that there exists a nonuniform grid that gives first-order convergent result, which is robust with respect to $\alpha$. Then a posteriori error estimation is derived and used to design an adaptive grid generation algorithm. Numerical results complement the theoretical findings.

主辦單位:大數據與人工智能學院