Recent Developments in Structure-Preserving Algorithms for Oscillatory Differential Equations

The main theme of thisbookis 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 thelatestadvances in the development of structure-preserving integrators for oscillatory differential equations, such as structure-preserving exponential integrators, functionally fitted energy-preserving integrators, exponential Fourier collocation methods, trigonometric collocation methods,andsymmetric and arbitrarily high-order time-stepping methods. Most of the material presented here is drawn from the recent literature. Theoretical analysis of the newly developed schemes shows their advantages in thecontextof structure preservation. All the new methods introduced in this bookare provento be highlyeffective compared with the well-known codes in the scientific literature. Thisbookalso addresseschallenging problems at the forefront of modern numerical analysis and presents a wide range of modern tools and techniques.