報告人：孫海衛(wèi) 教授
報告題目：All-at-once implementation of a time nonuniform mess scheme for sub-diffusion equation with initial time singularity
報告時間：2026年5月19日（周二）下午4:00—5:00
報告地點：云龍校區(qū)6號樓304報告廳
主辦單位：數(shù)學與統(tǒng)計學院、數(shù)學研究院、科學技術研究院
報告人簡介：
澳門大學數(shù)學系教授、博士生導師，1996年畢業(yè)于香港中文大學數(shù)學系獲得博士學位。主要研究領域包括數(shù)值線性代數(shù)、偏微分方程數(shù)值解和計算金融學等。在SIAM系列期刊SISC，SINUM，SIMAX，以及Numer Math、JCP、JSC等計算數(shù)學雜志發(fā)表超過120篇高水平研究論文，擔任過國際學術期刊EAJAM和IJCM編委，于2018年獲得澳門特區(qū)政府頒發(fā)的自然科學二等獎，共主持澳門科技發(fā)展基金6項。
報告摘要：
In this talk, the geometrically increased time step size (GITSS) is proposed to discretize the Caputo fractional derivative. The resulting coefficient matrix can be written as a product of a diagonal multiplying a lower triangular Toeplitz matrix. Coordinately, the resulting coefficient matrix of the discretized sub-diffusion equations is a block diagonal plus a block tridiagonal Toeplitz matrix, that can be implemented all-at-once using the divide-and-conquer strategy with the block forward substitution method efficiently. Theoretically, the convergence of the GITSS method with L1 scheme is proved, which is like that by the classical graded mesh scheme. Numerical results show the efficiency and availability of the all-at-once treatment by the proposed method. Moreover, the Toeplitz-like structure brought by the GITSS will have more potential to develop the fast algorithm in the future.