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【池州学院大讲堂】 刘利斌:Analysis of a finite difference scheme for a nonlinear Caputo fractional differential equation on an adaptive grid

发布日期:2021-05-12    作者:     来源:     点击:

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.

主办单位:大数据与人工智能学院