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W. Auzinger, A. Grosz, H. Hofstätter, O. Koch:
"Adaptive Time Propagation of the MCTDHF Equations";
Vortrag: SDIDE 2022 - 6th Workshop on Stability and Discretization Issues in Differential Equations, Budapest; 07.06.2022 - 10.06.2022.

We compare exponential-type integrators for the numerical
time-propagation of the equations of motion arising in the multiconfiguration
time-dependent Hartree-Fock method (MCTDHF) for solving the
high-dimensional multi-particle Schrödinger equation.

We find that among the most widely used integrators like Runge-Kutta, exponential
splitting, exponential Runge-Kutta, exponential multistep and Lawson methods,
exponential Lawson multistep methods with predictor/corrector
step provide optimal stability and accuracy at the least
computational cost, taking into account that the evaluation of the nonlocal
potential terms is by far the computationally most expensive part of such a calculation.

Moreover, the corrector step provides an estimator
for the time-stepping error at no additional cost, which enables adaptive time-stepping to reliably control the accuracy of a computation.