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Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations

  • Xinyuan Wu
  • Bin Wang

Table of contents

  1. Front Matter
    Pages i-xv
  2. Back Matter
    Pages 343-345

About this book

Introduction

The main theme of this book is recent progress in structure-preserving algorithms for solving initial value problems of oscillatory differential equations arising in a variety of research areas, such as astronomy, theoretical physics, electronics, quantum mechanics and engineering. It systematically describes the latest advances in the development of structure-preserving integrators for oscillatory differential equations, such as structure-preserving exponential integrators, functionally fitted energy-preserving integrators, exponential Fourier collocation methods, trigonometric collocation methods, and symmetric and arbitrarily high-order time-stepping methods. Most of the material presented here is drawn from the recent literature. Theoretical analysis of the newly developed schemes shows their advantages in the context of structure preservation. All the new methods introduced in this book are proven to be highly effective compared with the well-known codes in the scientific literature. This book also addresses challenging problems at the forefront of modern numerical analysis and presents a wide range of modern tools and techniques.

Keywords

structure-preserving exponential integrators functionally-fitted energy-preserving integrators exponential Fourier collocation methods trigonometric collocation methods symmetric and arbitrarily high-order time-stepping methods

Authors and affiliations

  • Xinyuan Wu
    • 1
  • Bin Wang
    • 2
  1. 1.Department of MathematicsNanjing UniversityNanjingChina
  2. 2.School of Mathematical SciencesQufu Normal UniversityQufuChina

Bibliographic information

  • DOI https://doi.org/10.1007/978-981-10-9004-2
  • Copyright Information Springer Nature Singapore Pte Ltd. And Science Press 2018
  • Publisher Name Springer, Singapore
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-981-10-9003-5
  • Online ISBN 978-981-10-9004-2
  • Buy this book on publisher's site
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