Geometric Integrators for Differential Equations with Highly Oscillatory Solutions

Focusing on the development of structure-preserving algorithms since the 1980s, this monograph delves into geometric numerical integration, particularly for highly oscillatory problems characterized by periodic or quasiperiodic solutions. It highlights the limitations of conventional methods for solving these equations over extensive time intervals. The work aims to advance the understanding and application of novel geometric integrators tailored for systems of ordinary and partial differential equations, addressing the growing significance of these techniques in mathematical dynamics.