Structure-preserving Algorithms For Oscillatory Differential Equations Ii
by Kai Liu /
2016 / English / PDF
13.3 MB Download
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 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.
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.