Structure-Preserving Algorithms for Oscillatory Differential Equations II

This book describes a variety of highly effective and efficient structure-preserving algorithms for second-order oscillatory differential equations. Such systems arise in many branches of science and engineering, and the examples in the book include systems from quantum physics, celestial mechanics...

Full description

Bibliographic Details
Published in:Springer eBooks
Main Authors: Wu, Xinyuan (Author), Liu, Kai (Author), Shi, Wei (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2015.
Edition:1st ed. 2015.
Subjects:
Online Access:http://dx.doi.org/10.1007/978-3-662-48156-1
Перейти в каталог НБ ТГУ
LEADER 04248nam a22005415i 4500
001 vtls000561960
003 RU-ToGU
005 20211110120932.0
007 cr nn 008mamaa
008 170213s2015 gw | s |||| 0|eng d
020 |a 9783662481561  |9 978-3-662-48156-1 
024 7 |a 10.1007/978-3-662-48156-1  |2 doi 
035 |a to000561960 
039 9 |y 201702130114  |z Александр Эльверович Гилязов  |b 100 
040 |a Springer  |c Springer  |d RU-ToGU 
050 4 |a TA329-348 
050 4 |a TA640-643 
072 7 |a TBJ  |2 bicssc 
072 7 |a MAT003000  |2 bisacsh 
082 0 4 |a 519  |2 23 
100 1 |a Wu, Xinyuan.  |e author.  |9 469315 
245 1 0 |a Structure-Preserving Algorithms for Oscillatory Differential Equations II  |h electronic resource  |c by Xinyuan Wu, Kai Liu, Wei Shi. 
250 |a 1st ed. 2015. 
260 |a Berlin, Heidelberg :  |b Springer Berlin Heidelberg :  |b Imprint: Springer,  |c 2015.  |9 742158 
300 |a XV, 298 p. 55 illus., 11 illus. in color.  |b online resource. 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
505 0 |a Matrix-variation-of-constants formula -- Improved St ¨ormer-Verlet formulae with applications -- Improved Filon-type asymptotic methods for highly oscillatory differential equations -- Efficient energy-preserving integrators for multi-frequency oscillatory Hamiltonian systems -- An extended discrete gradient formula for multi-frequency oscillatory Hamiltonian systems -- Trigonometric Fourier collocation methods for multi-frequency oscillatory systems -- Error bounds for explicit ERKN integrators for multi-frequency oscillatory systems -- Error analysis of explicit TSERKN methods for highly oscillatory systems -- Highly accurate explicit symplectic ERKN methods for multi-frequency oscillatory Hamiltonian systems -- Multidimensional ARKN methods for general multi-frequency oscillatory second-order IVPs -- A simplified Nystr¨om-tree theory for ERKN integrators solving oscillatory systems -- An efficient high-order explicit scheme for solving Hamiltonian nonlinear wave equations. 
520 |a This book describes a variety of highly effective and efficient structure-preserving algorithms for second-order oscillatory differential equations. Such systems arise in many branches of science and engineering, and the examples in the book include systems from quantum physics, celestial mechanics and electronics. To accurately simulate the true behavior of such systems, a numerical algorithm must preserve as much as possible their key structural properties: time-reversibility, oscillation, symplecticity, and energy and momentum conservation. The book describes novel advances in RKN methods, ERKN methods, Filon-type asymptotic methods, AVF methods, and trigonometric Fourier collocation methods.  The accuracy and efficiency of each of these algorithms are tested via careful numerical simulations, and their structure-preserving properties are rigorously established by theoretical analysis. The book also gives insights into the practical implementation of the methods. This book is intended for engineers and scientists investigating oscillatory systems, as well as for teachers and students who are interested in structure-preserving algorithms for differential equations. 
650 0 |a engineering.  |9 224332 
650 0 |a Computer mathematics.  |9 460896 
650 0 |a physics.  |9 566227 
650 0 |a Applied mathematics.  |9 460111 
650 0 |a Engineering mathematics.  |9 303575 
650 1 4 |a Engineering.  |9 224332 
650 2 4 |a Appl.Mathematics/Computational Methods of Engineering.  |9 303577 
650 2 4 |a Theoretical, Mathematical and Computational Physics.  |9 410498 
650 2 4 |a Computational Science and Engineering.  |9 304944 
700 1 |a Liu, Kai.  |e author.  |9 469316 
700 1 |a Shi, Wei  |e author.  |9 328245 
710 2 |a SpringerLink (Online service)  |9 143950 
773 0 |t Springer eBooks 
856 4 0 |u http://dx.doi.org/10.1007/978-3-662-48156-1 
856 |y Перейти в каталог НБ ТГУ  |u https://koha.lib.tsu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=416379 
912 |a ZDB-2-ENG 
950 |a Engineering (Springer-11647) 
999 |c 416379  |d 416379