Structure-Preserving Algorithms for Oscillatory Differential Equations II (inbunden)
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Format
Inbunden (Hardback)
Språk
Engelska
Antal sidor
298
Utgivningsdatum
2016-03-15
Upplaga
1st ed. 2015
Förlag
Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Illustratör/Fotograf
Bibliographie 40 schwarz-weiße und 1 farbige Abbildungen
Illustrationer
11 Illustrations, color; 44 Illustrations, black and white; XV, 298 p. 55 illus., 11 illus. in color
Dimensioner
242 x 157 x 23 mm
Vikt
754 g
Antal komponenter
1
Komponenter
1 Hardback
ISBN
9783662481554

Structure-Preserving Algorithms for Oscillatory Differential Equations II

av Xinyuan Wu, Kai Liu, Wei Shi
Inbunden,  Engelska, 2016-03-15
574
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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.
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Xinyuan Wu, Kai Liu, Wei Shi

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"This monograph is an excellent reference for practicing scientists and engineers who need in-depth information about structure-preserving integration of oscillatory ODEs. Senior undergraduate and graduate students of applied mathematics, engineering and physics will find the book to be an invaluable resource. It can also be used as a textbook in courses on structure preserving numerical algorithms for IVPs." (Martin Hermann, Mathematical Reviews, May, 2017) "The textbook demonstrates extensions and specialisations of numerical methods for the class of oscillatory problems given by second-order ordinary differential equations. This collection of scientific work is suitable for researchers as well as postgraduate students (Ph.D. students) in the field of numerical analysis." (Roland Pulch, zbMATH 1352.65187, 2017)

Innehållsförteckning

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 Nystrom-tree theory for ERKN integrators solving oscillatory systems.- An efficient high-order explicit scheme for solving Hamiltonian nonlinear wave equations.

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