报告题目：A second-order energy stable and nonuniform time-stepping scheme for time fractional Burgers' equation

报告人：任金城

报告时间：2024年07月28日（周日）上午10:00开始

报告地点：数学楼315会议室

报告摘要：In this talk, an effective finite difference scheme of high order accuracy is proposed for the nonlinear time fractional Burgers' equation. Specifically, we apply the Alikhanov's scheme on graded mesh in the temporal direction and a novel fourth-order compact scheme in the spatial discretization. The proposed scheme resolves initial weak singularity of the solution and preserves high resolution in the space direction, It is rigorously proved that the finite difference scheme is uniquely solvable, discrete variational energy dissipation law and unconditionally stable and convergent in sense of discrete L² norm. With appropriate choice of the grading parameter, the convergence accuracy is min{ra,2} order in time and fourth order in space, where r is the mesh grading. In the numerical implementation procedure, fast convolution technique and adaptive time-stepping strategy are adopted to accelerate the presented solver and to capture evolution of the solution. Numerical experiments are carried out to verify the validity and effectiveness of the proposed scheme for solving nonlinear time-fractional Burgers’ equation.

报告人简介：任金城，男，教授，华北水利水电大学博士生导师，河南财经政法大学数学与信息科学学院院长，国家级线上一流本科课程《数学建模方法与竞赛》负责人，河南省优秀教师，河南省文明教师，河南省优秀教学标兵，河南省教育厅学术技术带头人，全国大学生数学建模竞赛优秀指导教师，河南财经政法大学青年拔尖人才，河南财经政法大学教学名师，河南财经政法大学师德标兵。现主持国家自然科学基金面上项目1项，主持完成国家自然科学基金青年基金和天元基金项目各1项，主持河南省高校科技创新团队项目和河南省高校科技创新人才项目各1项，省厅级项目10余项。出版个人学术专著2部，在国际SCI期刊Journal of Computational Physics和Journal of Scientific Computing等杂志发表论文四十余篇。获河南省自然科学三等奖1项，河南省教育厅科技成果一等奖1项，河南省教育厅科技论文一等奖4项。主持省级及校级教学教育改革课题8项，指导学生参加美国大学生数学建模竞赛获国际二等奖以上30余项，指导学生参加全国大学生数学建模竞赛获国家奖、省级奖100余项。