Xinyuan Wu Knihy

Focusing on recent advancements, this book delves into structure-preserving algorithms tailored for oscillatory differential equations, relevant across fields like astronomy and quantum mechanics. It systematically reviews innovative integrators, including exponential and energy-preserving methods, alongside time-stepping techniques. Theoretical analyses highlight the benefits of these new approaches, demonstrating their effectiveness over traditional methods. Additionally, it tackles contemporary challenges in numerical analysis, offering a comprehensive array of modern tools and techniques.

Focusing on geometric numerical integration, this monograph delves into structure-preserving algorithms that emerged in the 1980s, emphasizing their role in identifying long-term behaviors and conservation laws in dynamic systems. It addresses the challenges posed by highly oscillatory problems, which involve periodic or quasiperiodic solutions across extensive time intervals. The work highlights the necessity for innovative geometric integrators tailored for both ordinary and partial differential equations, reflecting the growing significance of this area in contemporary mathematical research.

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 engineering. The book discusses novel advances in the ARKN, ERKN, two-step ERKN, Falkner-type and energy-preserving methods, etc. for oscillatory differential equations. The work is intended for scientists, engineers, teachers and students who are interested in structure-preserving algorithms for differential equations. Xinyuan Wu is a professor at Nanjing University; Xiong You is an associate professor at Nanjing Agricultural University; Bin Wang is a joint Ph. D student of Nanjing University and University of Cambridge.