Adaptive Exponential Integrators for MCTDHF

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11958)


We compare exponential-type integrators for the numerical time-propagation of the equations of motion arising in the multi-configuration time-dependent Hartree-Fock method for the approximation of 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 one 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 predictor 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.


Multi-configuration time-dependent Hartree-Fock method Time integration Splitting methods Exponential integrators Lawson methods Local error estimators Adaptive stepsize selection 


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Vienna University of TechnologyViennaAustria
  2. 2.Institute of MathematicsUniversity of ViennaViennaAustria

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