Overview
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
Includes supplementary material: sn.pub/extras
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Table of contents (12 chapters)
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Front Matter
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Back Matter
Keywords
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)
Authors and Affiliations
Bibliographic Information
Book Title: Structure-Preserving Algorithms for Oscillatory Differential Equations II
Authors: Xinyuan Wu, Kai Liu, Wei Shi
DOI: https://doi.org/10.1007/978-3-662-48156-1
Publisher: Springer Berlin, Heidelberg
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg and Science Press, Beijing, China 2015
Hardcover ISBN: 978-3-662-48155-4Published: 15 March 2016
Softcover ISBN: 978-3-662-56913-9Published: 25 April 2018
eBook ISBN: 978-3-662-48156-1Published: 03 March 2016
Edition Number: 1
Number of Pages: XV, 298
Number of Illustrations: 44 b/w illustrations, 11 illustrations in colour
Additional Information: Jointly published with Science Press, Beijing, China
Topics: Mathematical and Computational Engineering, Theoretical, Mathematical and Computational Physics, Computational Science and Engineering
Industry Sectors: Aerospace, Automotive, Biotechnology, Electronics, Energy, Utilities & Environment, Engineering, IT & Software, Oil, Gas & Geosciences, Telecommunications