报告人: Luigi Brugnano教授（Universita' degli Studi, Firenze意大利佛罗伦萨大学）

报告题目: Recent Advances on Line Integral Methods for Conservative Problems

报告摘要: Many problems deriving from applications, described by systems of differential equations, are characterized by constants of motion, representing relevant physical properties of the underlying dynamical systems, which are kept constant along the solution. In particular, Hamiltonian problems represent an important instance, and their numerical solution constitutes the core of what is nowadays named Geometric Integration. For canonical Hamiltonian problems, the most important constant of motion is the Hamiltonian function itself, which is often referred to as the “energy” of the system. For this reason, methods which are able to conserve the Hamiltonian are usually named energy-conserving.

 This short course is meant to provide a concise introduction to energy-conserving Runge-Kutta methods. The key tool exploited to devise these methods is what we have called “discrete line integral”: roughly speaking, one imposes energy conservation by requiring that a discrete counterpart of a line integral vanishes along the numerical solution regarded as a path in the phase space.

 The course will also cover some recent topics of research, including the numerical solution of Hamiltonian PDEs, as well as the devising of methods for constrained Hamiltonian problems.

 The lectures will be divided into the following six sections and each section will take two hours:

Section 1:  Basic notions about line integral methods

Section 2: Analysis of Hamiltonian Boundary Value Methods (HBVMs)

Section 3: Runge-Kutta form and efficient implementation of HBVMs

Section 4:  Hamiltonan PDEs: the semilinear wave equation

Section 5: Hamiltonan PDEs: the nonlinear Schroedinger equation

Section 6:  Constrained Hamiltonian systems and Energy and Quadratic Invariant methods.

报告时间和地点:

Section 1: 2017年5月20日上午9：30-11：30   (科技楼南楼702室)

Section 2: 2017年5月21日上午9：30-11：30   (科技楼南楼702室)

Section 3: 2017年5月22日上午9：30-11：30   (科技楼南楼702室)

Section 4-5: 2017年5月23日下午2：30-6：00  (东九楼D502室)

Section 6: 2017年5月24日上午9：30-11：30   (科技楼南楼702室)