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

报告人：刘利斌（博士、南宁师范大学副教授、硕士生导师）

时间：2021年5月12日（周三）16：00-17：00

地点：博奕南一楼会议室

报告人简介：

刘利斌，博士，南宁师范大学数学与统计学院副教授，硕士生导师，广西高等学校第二批千名骨干教师。主要研究兴趣为微分方程数值解、分数阶微分方程数值解及智能算法及其应用。主持完成国家自然科学基金3项，广西自然科学基金2项，安徽省高等学校优秀青年人才基金重点项目1项。迄今为止，在国内外高水平期刊上发表SCI论文近40篇。

内容提要：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.

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