报告题目：Numerical methods for Caputo-Hadamard fractional diffusion equations with weak singularity

报 告 人：汪志波 教授（广东工业大学）

报告时间：2022年10月18日9:00-10:30（星期二）

报告方式：腾讯会议703-971-980

报告摘要：In this talk, mathematical analysis and numerical methods for Caputo-Hadamard fractional diffusion equations with initial singularity are investigated. For the sub-diffusion case, a second-order scheme with nonuniform time meshes is investigated. we come up with an error convolution structure (ECS) analysis for $L2-1_{\sigma}$ interpolation approximation to the Caputo-Hadamard fractional derivative. The core result in this part is an ECS bound and a global consistency analysis established at an offset point. For the diffusion-wave case, we first obtain the analytical solution, the regularity and logarithmic decay of its solution are then researched. A fast compact scheme and a Crank-Nicolson scheme are then proposed for a equivalent model based on the technic of exponential type meshes. The final result that the error in numerically approximating the solution depends on the parameter $\gamma$ shows obviously how the regularity of the solution and the exponential type meshes affect the convergence order of the derived scheme.

个人简介：汪志波，博士，教授，广东省珠江人才计划-引进高层次人才，广东工业大学青年百人A类人才，《Mathematical Problems in Engineering》（SCI）和《中国理论数学前沿》期刊编委，广东省青年科学家协会理事，广东省计算数学会理事。主要从事偏微分方程数值解法等方面的研究。先后主持国家自然科学基金2项、广东省自然科学基金3项等10余项科研项目，以第一或通讯作者发表SCI论文40余篇，论文总引用量900余次，H指数17，i10指数21。