Structure-Preserving Algorithms for Oscillatory Differential Equations II

  • Xinyuan Wu
  • Kai Liu
  • Wei Shi

Table of contents

  1. Front Matter
    Pages i-xv
  2. Xinyuan Wu, Kai Liu, Wei Shi
    Pages 1-21
  3. Xinyuan Wu, Kai Liu, Wei Shi
    Pages 23-51
  4. Back Matter
    Pages 293-298

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.


ARKN Methods ERKN Methods Oscillatory Systems Second-order Oscillatory Differential Equations Structure-preserving Algorithms

Authors and affiliations

  • Xinyuan Wu
    • 1
  • Kai Liu
    • 2
  • Wei Shi
    • 3
  1. 1.Department of MathematicsNanjing UniversityNanjingChina
  2. 2.Nanjing University of Finance and EconomNanjingChina
  3. 3.Nanjing Tech UniversityNanjingChina

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg and Science Press, Beijing, China 2015
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-662-48155-4
  • Online ISBN 978-3-662-48156-1
  • Buy this book on publisher's site