東華大學圖書館 |

Language: English

Help

回圖書館首頁

手機版館藏查詢

Back

Switch To: Labeled | MARC Mode | ISBD

Geometric Numerical Integration and ...

Faou, Erwan,

Linked to FindBook

Google Book

Amazon

博客來

Geometric Numerical Integration and Schrödinger Equations

Record Type:	Electronic resources : Monograph/item
Title/Author:	Geometric Numerical Integration and Schrödinger Equations/ Erwan Faou
Author:	Faou, Erwan,
Published:	Zuerich, Switzerland :European Mathematical Society Publishing House, : 2012,
Description:	1 online resource (146 pages)
Subject:	Numerical analysis -
Online resource:	https://doi.org/10.4171/100
Online resource:	https://www.ems-ph.org/img/books/faou_mini.jpg
ISBN:	9783037196007

Geometric Numerical Integration and Schrödinger Equations
Faou, Erwan,

Geometric Numerical Integration and Schrödinger Equations[electronic resource] /Erwan Faou - Zuerich, Switzerland :European Mathematical Society Publishing House,2012 - 1 online resource (146 pages) - Zurich Lectures in Advanced Mathematics (ZLAM).

Restricted to subscribers:https://www.ems-ph.org/ebooks.php

The goal of geometric numerical integration is the simulation of evolution equations possessing geometric properties over long times. Of particular importance are Hamiltonian partial differential equations typically arising in application fields such as quantum mechanics or wave propagation phenomena. They exhibit many important dynamical features such as energy preservation and conservation of adiabatic invariants over long time. In this setting, a natural question is how and to which extent the reproduction of such long time qualitative behavior can be ensured by numerical schemes. Starting from numerical examples, these notes provide a detailed analysis of the Schrödinger equation in a simple setting (periodic boundary conditions, polynomial nonlinearities) approximated by symplectic splitting methods. Analysis of stability and instability phenomena induced by space and time discretization are given, and rigorous mathematical explanations for them. The book grew out of a graduate level course and is of interest to researchers and students seeking an introduction to the subject matter.

ISBN: 9783037196007

Standard No.: 10.4171/100doiSubjects--Topical Terms:

1245518
Numerical analysis

Geometric Numerical Integration and Schrödinger Equations
LDR:02137nmm a22003015a 4500 001 2233230
003 CH-001817-3
005 20111229234510.0
006 a fot ||| 0|
007 cr nn mmmmamaa
008 210928e20120114sz fot ||| 0|eng d
020 $a 9783037196007
024 7 0 $a 10.4171/100 $2 doi
035 $a 143-111229
040 $a ch0018173
072 7 $a PBS $2 bicssc
084 $a 65-xx $a 35-xx $a 37-xx $2 msc
100 1 $a Faou, Erwan, $e author. $3 3481025
245 1 0 $a Geometric Numerical Integration and Schrödinger Equations $h [electronic resource] / $c Erwan Faou
260 3 $a Zuerich, Switzerland : $b European Mathematical Society Publishing House, $c 2012
300 $a 1 online resource (146 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 0 $a Zurich Lectures in Advanced Mathematics (ZLAM)
506 1 $a Restricted to subscribers: $u https://www.ems-ph.org/ebooks.php
520 $a The goal of geometric numerical integration is the simulation of evolution equations possessing geometric properties over long times. Of particular importance are Hamiltonian partial differential equations typically arising in application fields such as quantum mechanics or wave propagation phenomena. They exhibit many important dynamical features such as energy preservation and conservation of adiabatic invariants over long time. In this setting, a natural question is how and to which extent the reproduction of such long time qualitative behavior can be ensured by numerical schemes. Starting from numerical examples, these notes provide a detailed analysis of the Schrödinger equation in a simple setting (periodic boundary conditions, polynomial nonlinearities) approximated by symplectic splitting methods. Analysis of stability and instability phenomena induced by space and time discretization are given, and rigorous mathematical explanations for them. The book grew out of a graduate level course and is of interest to researchers and students seeking an introduction to the subject matter.
650 0 7 $a Numerical analysis $3 1245518
650 0 7 $a Partial differential equations $2 msc. $3 1597893
650 0 7 $a Dynamical systems and ergodic theory $2 msc $3 3480821
856 4 0 $u https://doi.org/10.4171/100
856 4 2 $3 cover image $u https://www.ems-ph.org/img/books/faou_mini.jpg