Structure-Preserving Algorithms for Oscillatory Differential Equations II

This book focuses on structure-preserving algorithms for initial value problems involving systems of oscillatory differential equations and characterized by its rigorous mathematical analysis, deep insights into practical computation and informative illustrations. The large number of highly effective and efficient structure-preserving algorithms for multi-frequency oscillatory second-order differential equations with theoretical analysis and numerical validation presented in this book will be of particular interest to the readers. Since a variety of problems in fields such as applied mathematics, mechanics, electronics, celestial mechanics, quantum physics and engineering share special properties like oscillation, symplecticity, time-reversibility, energy and momentum preservation, etc., numerical simulations are expected to preserve these important properties as much as possible. Readers will be familiarized with the latest advances in multi-frequency ARKN methods and ERKN methods, error bounds of the explicit ERKN integrators and two-step ERKN integrators, trigonometric Fourier collocation methods, extended discrete gradient methods, coupled conditions of symplecticity and symmetry of ERKN methods etc. for multi-frequency oscillatory differential equations with multiple time scales. Theoretical analysis of the newly developed schemes shows their advantages in structure preservation. All the novel integrators are proved to be highly effective and competitive compared with the existing integrators when applied to the classical test problems in the scientific literature.§