Structure-Preserving Algorithms for Oscillatory Differential Equations II, 1st ed. 2015

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.

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