勷勤数学•专家报告

题      目：Modified BDF convolution quadrature for multi-singularity problems arising from delay fractional diffusion-wave equations

报  告  人： 黄锡荣 教授  (邀请人：陈小山)

                                    澳门大学

时      间： 6月15日  16：00-17:00

地     点：数科院东楼401

报告人简介:

        黄锡荣：澳门大学科技学院博导，教授。主要研究方向：数值线性代数、数值微分方程、优化与控制论等领域。在SIAM Journal on Matrix analysis and Applications.、Journal of Differential Equations、Journal of Computational Physics等期刊发表学术论文120余篇。研究成果分别获2016年和2022年澳门自然科学奖二等奖和三等奖。

摘      要：

       In this talk, we focus on the pointwise-in-time error estimates for fractional diffusion-wave equations in the presence of time delay. The semi-discrete solution is derived through the convolution quadrature with the generating function given by kappa-step BDF (kappa = 1, 2, 3). For the sake of restoring the desired kappa-th-order convergence accuracy of BDFkappa, the proper correction formula at the starting kappa-1 steps is developed. Theoretical result shows that the convergence order is min{(kappa + 1)alpha, kappa} at (kappa.tau)+, whereas it is alpha at 0+, where kappa \in N+, tau is delay factor, and alpha ∈ (1, 2) is the fractional order. Some numerical tests are given to justify the theoretical results.

          欢迎老师、同学们参加、交流！