A fourth-order Magnus scheme for Helmholtz equation
Journal of Computational and Applied Mathematics
New methods for oscillatory systems based on ARKN methods
Applied Numerical Mathematics
Applied Numerical Mathematics
The LEM exponential integrator for advection-diffusion-reaction equations
Journal of Computational and Applied Mathematics
A second-order Magnus-type integrator for nonautonomous parabolic problems
Journal of Computational and Applied Mathematics
A Globalized Newton Method for the Accurate Solution of a Dipole Quantum Control Problem
SIAM Journal on Scientific Computing
Time-averaging and exponential integrators for non-homogeneous linear IVPs and BVPs
Applied Numerical Mathematics
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Numerical methods based on the Magnus expansion are an efficient class of integrators for Schrödinger equations with time-dependent Hamiltonian. Though their derivation assumes an unreasonably small time step size, as would be required for a standard explicit integrator, the methods perform well even for much larger step sizes. This favorable behavior is explained, and optimal-order error bounds are derived that require no or only mild restrictions of the step size. In contrast to standard integrators, the error does not depend on higher time derivatives of the solution, which is in general highly oscillatory.