报告时间：2024年6月7日（星期五）15:00-16:00

报告地点：翡翠科教楼B1710

报告人：廖锋 副教授

工作单位：常熟理工学院

举办单位：数学学院

报告简介：

This talk is concerned with the numerical solutions of Schrödinger-Boussinesq (SBq) system by an orthogonal spline collocation (OSC) discretization in space and Crank-Nicolson (CN) type approximation in time. By using the mathematical induction argument and standard energy method, the proposed CN+OSC scheme is proved to be unconditionally convergent at the order with mesh-size and time step in the discrete-norm. We devise a new computation method based on the orthogonal diagonalization techniques (ODT) to realize the proposed CN+OSC scheme. In order to compare the performance of ODT, we devise an alternating direction implicit (ADI) method to compute the CN+OSC scheme for high spatial dimension SBq system. As an alternative implementation, the new method ODT not only exhibits more accurate numerical results, but also demonstrates stronger invariance preserving ability. Numerical results are reported to verify the error estimates and the discrete conservation laws.

报告人简介：

廖锋，常熟理工学院副教授。2018年南京航空航天大学取得博士学位后入职常熟理工学院。廖锋博士主要从事偏微分方程保结构算法的相关研究，在Journal of Computational and Applied Mathematics, Applied Numerical Mathematics, Calcolo,Communications in Nonlinear Science and Numerical Simulation等刊物发表论文20余篇。