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Structure-Preserving Algorithms for Oscillatory Differential Equations II

Authors: Wu, Xinyuan, Liu, Kai, Shi, Wei

  • Includes recent advances in the ARKN methods, ERKN methods, two-step ERKN methods, trigonometric Fourier collocation methods, energy-preserving methods etc.
  • Includes new and important development of the error analysis for ERKN methods and two-step ERKN methods
  • Lays emphasis on the structure-preserving properties and computational efficiency of newly developed integrators
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Buy this book

eBook 83,29 €
price for China (P.R.) (gross)
  • ISBN 978-3-662-48156-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 99,99 €
price for China (P.R.) (gross)
  • ISBN 978-3-662-48155-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

Reviews

“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)


Table of contents (12 chapters)

  • Matrix-Variation-of-Constants Formula

    Wu, Xinyuan (et al.)

    Pages 1-21

    Preview Buy Chapter 24,95 €
  • Improved Störmer–Verlet Formulae with Applications

    Wu, Xinyuan (et al.)

    Pages 23-51

    Preview Buy Chapter 24,95 €
  • Improved Filon-Type Asymptotic Methods for Highly Oscillatory Differential Equations

    Wu, Xinyuan (et al.)

    Pages 53-68

    Preview Buy Chapter 24,95 €
  • Efficient Energy-Preserving Integrators for Multi-frequency Oscillatory Hamiltonian Systems

    Wu, Xinyuan (et al.)

    Pages 69-93

    Preview Buy Chapter 24,95 €
  • An Extended Discrete Gradient Formula for Multi-frequency Oscillatory Hamiltonian Systems

    Wu, Xinyuan (et al.)

    Pages 95-115

    Preview Buy Chapter 24,95 €

Buy this book

eBook 83,29 €
price for China (P.R.) (gross)
  • ISBN 978-3-662-48156-1
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 99,99 €
price for China (P.R.) (gross)
  • ISBN 978-3-662-48155-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Structure-Preserving Algorithms for Oscillatory Differential Equations II
Authors
Copyright
2015
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg and Science Press, Beijing, China
Distribution Rights
Distribution rights for print copies in China: Science Press
eBook ISBN
978-3-662-48156-1
DOI
10.1007/978-3-662-48156-1
Hardcover ISBN
978-3-662-48155-4
Edition Number
1
Number of Pages
XV, 298
Number of Illustrations and Tables
44 b/w illustrations, 11 illustrations in colour
Additional Information
Jointly published with Science Press, Beijing, China
Topics