Geometric Integrators for Differential Equations with Highly Oscillatory Solutions

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.