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(xué)副教授、碩士生導(dǎo)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：

劉利斌，博士，南寧師范大學(xué)數(shù)學(xué)與統(tǒng)計學(xué)院副教授，碩士生導(dǎo)師，廣西高等學(xué)校第二批千名骨干教師。主要研究興趣為微分方程數(shù)值解、分?jǐn)?shù)階微分方程數(shù)值解及智能算法及其應(yīng)用。主持完成國家自然科學(xué)基金3項，廣西自然科學(xué)基金2項，安徽省高等學(xué)校優(yōu)秀青年人才基金重點項目1項。迄今為止，在國內(nèi)外高水平期刊上發(fā)表SCI論文近40篇。

內(nèi)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(shù)據(jù)與人工智能學(xué)院