The Magnus expansion and some of its applications
comunitat-uji-handle:10234/9
comunitat-uji-handle2:10234/7037
comunitat-uji-handle3:10234/8635
comunitat-uji-handle4:
INVESTIGACIONAquest recurs és restringit
http://dx.doi.org/10.1016/j.physrep.2008.11.001 |
Metadades
Títol
The Magnus expansion and some of its applicationsData de publicació
2009Editor
ElsevierISSN
3701573Cita bibliogràfica
Physics Reports, 470, , p. 151-238Tipus de document
info:eu-repo/semantics/reviewVersió
info:eu-repo/semantics/publishedVersionResum
Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem, shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control ... [+]
Approximate resolution of linear systems of differential equations with varying coefficients is a recurrent problem, shared by a number of scientific and engineering areas, ranging from Quantum Mechanics to Control Theory. When formulated in operator or matrix form, the Magnus expansion furnishes an elegant setting to build up approximate exponential representations of the solution of the system. It provides a power series expansion for the corresponding exponent and is sometimes referred to as Time-Dependent Exponential Perturbation Theory. Every Magnus approximant corresponds in Perturbation Theory to a partial re-summation of infinite terms with the important additional property of preserving, at any order, certain symmetries of the exact solution. The goal of this review is threefold. First, to collect a number of developments scattered through half a century of scientific literature on Magnus expansion. They concern the methods for the generation of terms in the expansion, estimates of the radius of convergence of the series, generalizations and related non-perturbative expansions. Second, to provide a bridge with its implementation as generator of especial purpose numerical integration methods, a field of intense activity during the last decade. Third, to illustrate with examples the kind of results one can expect from Magnus expansion, in comparison with those from both perturbative schemes and standard numerical integrators. We buttress this issue with a revision of the wide range of physical applications found by Magnus expansion in the literature. © 2008 Elsevier B.V. All rights reserved. [-]
Drets d'accés
http://rightsstatements.org/vocab/InC/1.0/
info:eu-repo/semantics/restrictedAccess
info:eu-repo/semantics/restrictedAccess
Apareix a les col.leccions
- MAT_Articles [745]