| Issue |
ESAIM: M2AN
Volume 53, Number 6, November-December 2019
|
|
|---|---|---|
| Page(s) | 2109 - 2119 | |
| DOI | https://doi.org/10.1051/m2an/2019033 | |
| Published online | 12 December 2019 | |
Convergence of exponential Lawson-multistep methods for the MCTDHF equations
Universität Wien, Fakultät für Mathematik, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria
* Corresponding author: othmar@othmar-koch.org
Received:
30
March
2018
Accepted:
25
April
2019
We consider exponential Lawson multistep methods for the time integration of the equations of motion associated with the multi-configuration time-dependent Hartree–Fock (MCTDHF) approximation for high-dimensional quantum dynamics. These provide high-order approximations at a minimum of evaluations of the computationally expensive nonlocal potential terms, and have been found to enable stable long-time integration. In this work, we prove convergence of the numerical approximation on finite time intervals under minimal regularity assumptions on the exact solution. A numerical illustration shows adaptive time propagation based on our methods.
Mathematics Subject Classification: 65L05 / 65L06 / 65M12 / 65M15 / 65M20 / 81-08
Key words: Multi-configuration time-dependent Hartree–Fock method / exponential Lawson multistep methods / stability / local error / convergence
© EDP Sciences, SMAI 2019
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