Structure-Preserving Algorithms for Oscillatory Differential Equations

From the reviews:“The monograph contains a detailed discussion of the class of numerical integrators for oscillatory problems defined by second-order ordinary differential equations. This work is suitable for researchers as well as for students in the field of numerical analysis.” (Roland Pulch, zbMATH, Vol. 1276, 2014)“In this monograph the authors present structure-preserving ODE-solvers for oscillatory IVPs that arise in a wide range of fields such as astronomy, natural sciences and engineering. … This book is an excellent reference for practicing scientists and engineers who need in-depth information about structure-preserving integration of oscillatory ODEs.” (Martin Hermann, Mathematical Reviews, December, 2013)

• Runge-Kutta (-Nyström) Methods for Oscillatory Differential Equations.- ARKN Methods.- ERKN Methods.- Symplectic and Symmetric Multidimensional ERKN Methods.- Two-Step Multidimensional ERKN Methods.- Adapted Falkner-Type Methods.- Energy-Preserving ERKN Methods.- Effective Methods for Highly Oscillatory Second-Order Nonlinear Differential Equations.- Extended Leap-Frog Methods for Hamiltonian Wave Equations.