×

Efficient computation of the Airy propagators. (English) Zbl 1196.81062

Summary: We construct a new set of formulae for the Airy propagators whose computation is by one order of magnitude faster than that based on the Airy functions, with the additional advantage of producing results which are free of accuracy loss. The new set can be successfully applied, among others, for improving the performance of the codes which use the method of Gordon for the solution of the Schrödinger equation.

MSC:

81-08 Computational methods for problems pertaining to quantum theory
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
35Q55 NLS equations (nonlinear Schrödinger equations)

Software:

SLCPM12; NAG; CRCWFN; nag
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Gordon, R. G., J. Chem. Phys., 51, 14 (1969)
[2] Gordon, R. G., (Methods in Computational Physics, vol. 10 (1971), Academic Press), 81
[3] Alexander, M. H., J. Chem. Phys., 81, 4510 (1984)
[4] Alexander, M. H.; Manolopoulos, D. E., J. Chem. Phys., 86, 2044 (1987)
[5] Alexander, M. H., Comput. Phys. Comm., 75, 87 (1993)
[6] Ixaru, L. Gr., Numerical Methods for Differential Equations and Applications (1984), Reidel: Reidel Dordrecht, Boston, Lancaster · Zbl 0301.34010
[7] Ixaru, L. Gr.; De Meyer, H.; Vanden Berghe, G., J. Comput. Appl. Math., 88, 289 (1997)
[8] Ixaru, L. Gr.; De Meyer, H.; Vanden Berghe, G., Comput. Phys. Comm., 118, 259 (1999)
[9] Ixaru, L. Gr., J. Comput. Appl. Math., 125, 347 (2000)
[10] Ledoux, V.; Rizea, M.; Ixaru, L. Gr.; Vanden Berghe, G.; Van Daele, M., Comput. Phys. Comm., 175, 424 (2006)
[11] Abramowitz, M.; Stegun, I. A., Handbook of Mathematical Functions (1972), Dover: Dover New York · Zbl 0515.33001
[12] Vallée, O.; Soares, M., Airy Functions and Applications to Physics (2004), Imperial College Press: Imperial College Press London · Zbl 1056.33006
[13] Christley, J. A.; Thompson, I. J., Comput. Phys. Comm., 79, 143 (1994)
[14] Fabijonas, B. R., ACM Trans. Math. Softw., 30, 491 (2004)
[15] NAG Fortran Library Manual Mark 15, The Numerical Algorithms Group Limited, Oxford, 1991; NAG Fortran Library Manual Mark 15, The Numerical Algorithms Group Limited, Oxford, 1991
[16] Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P., Numerical Recipes in Fortran—The Art of Scientific Computing (1996), Cambridge University Press · Zbl 0892.65001
[17] Zhang, S.; Jin, J. M., Computation of Special Functions (1996), John Wiley & Sons: John Wiley & Sons New York
[18] J.M. Hutson, S. Green, MOLSCAT computer code, version 14, 1994, distributed by Collaborative Computational Project No. 6 of the Engineering and Physical Sciences Research Council (UK); J.M. Hutson, S. Green, MOLSCAT computer code, version 14, 1994, distributed by Collaborative Computational Project No. 6 of the Engineering and Physical Sciences Research Council (UK)
[19] Ixaru, L. Gr., Phys. Rev. D, 25, 1557 (1982)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.