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W. Auzinger, A. Grosz, H. Hofstätter, O. Koch:
"Efficient adaptive time integrators for high-dimensional Schrödinger equations";
Talk: Workshop on Numerical Solution of Integral and Differential Equations (NSIDE 2019), Gdansk (invited); 2019-07-17 - 2019-07-19.

We present efficient adaptive numerical solution methods for systems of nonlinear
Schrödinger equations associated with the multiconfiguration time-dependent
Hartree-Fock method for the solution of the multi-electron time-dependent Schrödinger
equation. The methods in our focus comprise splitting methods, exponential integrators
and Lawson methods. We demonstrate that in the light of the high computational
effort for the evaluation of the nonlocal operator associated with the potential
part, Adams-Lawson multistep methods with a predictor/corrector step provide an
optimal work/precision relation and also stable long-term integration. The corrector
also provides an error estimator without additional computational effort, and
thus adaptive time-stepping can be realized. This is demonstrated to reflect well the
smoothness of the solution. Furthermore, the convergence of Adams-Lawson multistep
methods for the MCTDHF equations is proven theoretically under minimal
assumptions on the regularity of the exact solution.