Chebyshev-Approximation for Wavepacket-Dynamics: better than expected

Please always quote using this URN: urn:nbn:de:0297-zib-2575
  • The aim of this work is to study the accuracy and stability of the Chebyshev--approximation method as a time--discretization for wavepacket dynamics. For this frequently used discretization we introduce estimates of the approximation and round--off error. These estimates mathematically confirm the stability of the Chebyshev--approximation with respect to round--off errors, especially for very large stepsizes. But the results also disclose threads to the stability due to large spatial dimensions. All theoretical statements are illustrated by numerical simulations of an analytically solvable example, the harmonic quantum oszillator.

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Metadaten
Author:Peter Nettesheim, Wilhelm Huisinga, Christof Schütte
Document Type:ZIB-Report
Date of first Publication:1996/12/02
Series (Serial Number):ZIB-Report (SC-96-47)