走向现代数学学术报告 – 孙海卫教授（No. 991)

报告题目：Exponential Runge-Kutta integrators with τ-stiff-cutter for fractional Laplacian semilinear diffusion equations

报 告 人：孙海卫 教授（澳门大学）

邀 请 人：林福荣 教授

报告时间：2026年11月20日 14：00

报告地点：东海岸校区D209

报告摘要：In this talk, we study the exponential Runge-Kutta integrators with τ-stiff-cutter for numerical solutions of the multi-dimemsional fractional Laplacian semilinear diffusion equations. Once the space-fractional Laplacian operator is discretized using a second-order fractional centered difference method, we obtain a semilinear system of the ODEs, where the linear term is stiff and possesses a multi-level Toeplitz structure. We then split the linear term into two parts. The first part (i.e., τ matrix) is treated exactly, while explicit treatment is adopted for the second part and the remaining nonlinear term. Based on this process, the exponential Runge-Kutta integrators are proposed to approximate the splitting semilinear system of the ODEs. The main advantage of our new method is that it enables the efficient evaluation of the related ϕ functions of τ matrix arising from the accelerated exponential Runge-Kutta integrators. Theoretically, we establish an error estimate for the second-order accelerated exponential Runge-Kutta integrator in the discrete sense. Numerical experiments are conducted to highlight the computational effectiveness and confirm the theoretical results of the proposed method.

报告人简介：孙海卫，澳门大学数学系教授、博士生导师，1996年毕业于香港中文大学数学系获得博士学位。主要研究领域包括数值线性代数、偏微分方程数值解、和计算金融学等。在SISC，SINUM，SIMAX，JCP等计算数学杂志发表超过130篇高水平研究论文，担任过国际学术期刊EAJAM, IJCM和AMC编委，于2018年获得澳门特区政府颁发的自然科学二等奖，在2019年第8届华人数学家大会（ICCM）作45分钟大会报告，共主持澳门科技发展基金6项。