报告人：Luigi Brugnano（佛罗伦萨大学）
邀请人：黄乘明
报告时间：Section one: 2024年4月17日（星期三）15：00-17：00
Section two: 2024年4月18日（星期四）15：00-17：00
Section three: 2024年4月19日（星期五）9：30-11：30
Section four: 2024年4月20日（星期六）9：30-11：30
Section five: 2024年4月21日（星期日）9：30-11：30
报告地点：科技楼南楼702室
报告题目：Line Integral Methods and some extensions
报告摘要：The framework of Line Integral Methods has been initially devised to derive energy-conserving methods for Hamiltonian problems (see, e.g., the monograph [4], the review paper [5], and references therein). It became soon clear that the methods could be easily obtained through a local Fourier expansion of the vector field along the Legendre polynomial basis, eventually resulting in the so called Hamiltonian Boundary Value Methods (HBVMs), which is a class of low-rank Runge-Kutta methods. This expansion, coupled with the availability of a very effective nonlinear iteration for solving the generated discrete problems [7], has in turn allowed their use as spectral methods in time [1, 8, 9]. Moreover, this has allowed to extend the approach to cope with a variety of problems, as is sketched in [6]. In particular, in these lectures the basic facts about this approach will be recalled, along with their recent extension for numerically solving fractional differential equations [2, 3].
This lecture series will be divided into the following five sections:
Section One: Line Integral Methods and energy conservation in Hamiltonian problems;
Section Two: Analysis of Line Integral Methods;
Section Three: Runge-Kutta form and Hamiltonian Boundary Value Methods (HBVMs);
Section Four: HBVMs as spectral methods in time (SHBVMs)
Section Five: Fractional Hamiltonian Boundary Value Methods (FHBVMs).
报告人简介：Luigi Brugnano，意大利佛罗伦萨大学理学院教授。发表论文150余篇，专著5本，具体目录参见下面链接https://people.dimai.unifi.it/brugnano/files/elenpub.html。担任期刊Journal of Computational and Applied Mathematics主编;Applied Mathematics and Computations，Applied Numerical Mathematics等十余个国际期刊编委。
