Symplectic integrators for second-order linear non-autonomous equations
For researchers solving time-dependent linear systems, particularly wave equations, this provides specialized symplectic methods that improve efficiency and accuracy over general-purpose integrators.
The paper presents two families of symplectic integrators for second-order linear non-autonomous systems, derived from the Magnus expansion, tailored for low-to-moderate and large dimensions (e.g., discretized wave equations). Numerical experiments demonstrate their effectiveness.
Two families of symplectic methods specially designed for second-order time-dependent linear systems are presented. Both are obtained from the Magnus expansion of the corresponding first-order equation, but otherwise they differ in significant aspects. The first family is addressed to problems with low to moderate dimension, whereas the second is more appropriate when the dimension is large, in particular when the system corresponds to a linear wave equation previously discretised in space. Several numerical experiments illustrate the main features of the new schemes.