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【学术报告】2024年4月17-21日Luigi Brugnano教授来我院举办系列学术讲座

时间:2024-04-16

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 ComputationsApplied Numerical Mathematics等十余个国际期刊编委。



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