02411nam a22003615a 4500001001100000003001200011005001700023006001900040007001500059008004100074020001800115024002100133040001400154072001600168084002900184100002600213245010000239260008200339300003400421336002600455337002600481338003600507347002400543490005100567506006600618520112400684650003101808650002801839650004001867650004601907856003201953856006401985143-111229CH-001817-320111229234510.0a fot ||| 0|cr nn mmmmamaa111229e20120114sz fot ||| 0|eng d a978303719600770a10.4171/1002doi ach0018173 7aPBS2bicssc a65-xxa35-xxa37-xx2msc1 aFaou, Erwan,eauthor.10aGeometric Numerical Integration and SchrÃ¶dinger Equationsh[electronic resource] /cErwan Faou3 aZuerich, Switzerland :bEuropean Mathematical Society Publishing House,c2012 a1 online resource (146 pages) atextbtxt2rdacontent acomputerbc2rdamedia aonline resourcebcr2rdacarrier atext filebPDF2rda0 aZurich Lectures in Advanced Mathematics (ZLAM)1 aRestricted to subscribers:uhttps://www.ems-ph.org/ebooks.php aThe 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
SchrÃ¶dinger 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.07aNumerical analysis2bicssc07aNumerical analysis2msc07aPartial differential equations2msc07aDynamical systems and ergodic theory2msc40uhttps://doi.org/10.4171/100423cover imageuhttps://www.ems-ph.org/img/books/faou_mini.jpg