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Geometric Numerical Integration and ...

Faou, Erwan,

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Geometric Numerical Integration and Schrödinger Equations

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Geometric Numerical Integration and Schrödinger Equations/ Erwan Faou
作者:	Faou, Erwan,
出版者:	Zuerich, Switzerland :European Mathematical Society Publishing House, : 2012,
面頁冊數:	1 online resource (146 pages)
標題:	Numerical analysis -
電子資源:	https://doi.org/10.4171/100
電子資源:	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
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