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, oscillatio...

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 f...

Structure-Preserving Algorithms for Oscillatory Differential Equations describes a large number of highly effective and efficient structure-preserving algorithms for second-order oscillatory differential equations by using theoretical analysis and numerical validation. Structure-preserving algorithms for differential equations, especially for oscillatory differential equations, play an important role in the accurate simulation of oscillatory problems in applied sciences and engine...

The idea of structure-preserving algorithms appeared in the 1980's. The new paradigm brought many innovative changes. The new paradigm wanted to identify the long-time behaviour of the solutions or the existence of conservation laws or some other qualitative feature of the dynamics. Another area that has kept growing in importance within Geometric Numerical Integration is the study of highly-oscillatory problems: problems where the solutions are periodic or quasiperiodic and have to be stu...

This book explores how genomic data are revolutionising basic and applied invasion science. It shows how genomic technologies can reveal key drivers of biological invasions, such as hybridisation and rapid adaptation, and illustrates major breakthroughs achieved through the study of model systems. Multiple layers of variation are considered, including epigenetic variation and genetic variation, from chromosomal rearrangements to single nucleotide polymorphisms. Applied topics emphasise sta...

China in the Era of Social Media discusses how social media is changing the world in an unprecedented way through speed, scope, and depth. In the last decade or so, social media in China has witnessed the most explosive growth in the world. Being the most populous nation in the world, it has the most social media users in the world as well. This book examines the current situation and unique characteristics of Chinese social media, the significance of social media in the country’s...