On the Global Error of Discretization Methods for Highly-Oscillatory Ordinary Differential Equations

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Adiabatic Integrators for Highly Oscillatory Second-Order Linear Differential Equations with Time-Varying Eigendecomposition (2005, methodology): “• the modified Magnus method of classical order 4 as presented by Iserles [ 8 ].”
The Magnus expansion and some of its applications (2008, background): “This approach has been considered in [115,116], and shows an extraordinary improvement when the system is highly oscillatory and the main oscillatory part is integrated with Ỹ0.”
Highly Oscillatory Quadrature: The Story soFar (2006, methodology): “It is thus of interest to mention that the availability of efficient highly oscillatory quadrature is critical to a number of contemporary methods for ordinary differential equations that exhibit rapid oscillation (Degani & Schiff 2003, Iserles 2002, Iserles 2004, Lorenz, Jahnke & Lubich 2005).”
Fourth-and sixth-order commutator-free Magnus integrators for linear and non-linear dynamical systems (2006, methodology): “This procedure is closely related to the modified Magnus integrators in [16] where the dominant constant term is factorized.”
Exponential integrators (2010, unknown): “Related numerical integrators for highly oscillatory ordinary differential equations are discussed in Iserles (2002a, 2002b); an application to electronic engineering is given in Condon, Deaño and Iserles (2009).”