Structure-Preserving Algorithms for Oscillatory Differential Equations

Authors: Wu, Xinyuan, You, Xiong, Wang, Bin

  • Includes recent advances in the ARKN methods, ERKN methods, two-step ERKN methods, energy-preserving methods, etc.
  • Focuses on new and important development of rooted-tree and B-series theories with applications in derivation of order conditions for new RKN-type methods
  • Places emphasis on the structure-preserving properties and computational efficiency of newly developed integrators
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About this book

Structure-Preserving Algorithms for Oscillatory Differential Equations describes a large number of highly effective and efficient structure-preserving algorithms for second-order oscillatory differential equations by using theoretical analysis and numerical validation. Structure-preserving algorithms for differential equations, especially for oscillatory differential equations, play an important role in the accurate simulation of oscillatory problems in applied sciences and engineering. The book discusses novel advances in the ARKN, ERKN, two-step ERKN, Falkner-type and energy-preserving methods, etc. for oscillatory differential equations.

The work is intended for scientists, engineers, teachers and students who are interested in structure-preserving algorithms for differential equations. Xinyuan Wu is a professor at Nanjing University; Xiong You is an associate professor at Nanjing Agricultural University; Bin Wang is a joint Ph.D student of Nanjing University and University of Cambridge.

Reviews

From the reviews:

“The monograph contains a detailed discussion of the class of numerical integrators for oscillatory problems defined by second-order ordinary differential equations. This work is suitable for researchers as well as for students in the field of numerical analysis.” (Roland Pulch, zbMATH, Vol. 1276, 2014)

“In this monograph the authors present structure-preserving ODE-solvers for oscillatory IVPs that arise in a wide range of fields such as astronomy, natural sciences and engineering. … This book is an excellent reference for practicing scientists and engineers who need in-depth information about structure-preserving integration of oscillatory ODEs.” (Martin Hermann, Mathematical Reviews, December, 2013)


Table of contents (10 chapters)

  • Runge–Kutta (–Nyström) Methods for Oscillatory Differential Equations

    Wu, Xinyuan (et al.)

    Pages 1-25

  • ARKN Methods

    Wu, Xinyuan (et al.)

    Pages 27-61

  • ERKN Methods

    Wu, Xinyuan (et al.)

    Pages 63-90

  • Symplectic and Symmetric Multidimensional ERKN Methods

    Wu, Xinyuan (et al.)

    Pages 91-119

  • Two-Step Multidimensional ERKN Methods

    Wu, Xinyuan (et al.)

    Pages 121-149

Buy this book

eBook $119.00
price for USA (gross)
  • ISBN 978-3-642-35338-3
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $159.00
price for USA
  • ISBN 978-3-642-35337-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Structure-Preserving Algorithms for Oscillatory Differential Equations
Authors
Copyright
2013
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Science Press Beijing and Springer-Verlag Berlin Heidelberg
Distribution Rights
Distribution rights in China Science Press
eBook ISBN
978-3-642-35338-3
DOI
10.1007/978-3-642-35338-3
Hardcover ISBN
978-3-642-35337-6
Edition Number
1
Number of Pages
XII, 236
Number of Illustrations and Tables
38 b/w illustrations, 2 illustrations in colour
Additional Information
Jointly published with Science Press Beijing
Topics