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Journal

2011 | 9 | 6 | 1518-1535

Article title

Optimizing a class of linear multi-step methods for the approximate solution of the radial Schrödinger equation and related problems with respect to phase-lag

Authors

Content

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Languages of publication

EN

Abstracts

EN
In this paper we consider a methodology of optimization of the efficiency of a numerical method for the approximate solution of the radial Schrödinger equation and related problems. More specifically, we show how the methodology of vanishing of the phase-lag and its derivatives optimizes the behaviour of a numerical method.

Publisher

Journal

Year

Volume

9

Issue

6

Pages

1518-1535

Physical description

Dates

published
1 - 12 - 2011
online
15 - 10 - 2011

References

  • [1] L. G. Ixaru, M. Micu, Topics in Theoretical Physics (Central Institute of Physics, Bucharest, 1978)
  • [2] L. D. Landau, F. M. Lifshitz, Quantum Mechanics (Pergamon, New York, 1965)
  • [3] T. E. Simos, P. S. Williams, On finite difference methods for the solution of the Schrodinger equation, Comput. Chem. 23, 513 (1999) http://dx.doi.org/10.1016/S0097-8485(99)00023-6[Crossref]
  • [4] A. D. Raptis, Exponential multistep methods for ordinary differential equations, Bulletin of the Greek Mathematical Society 25, 113 (1984).
  • [5] L. G. Ixaru, Numerical Methods for Differential Equations and Applications (Reidel, Dordrecht - Boston - Lancaster, 1984)
  • [6] L. G. Ixaru, M Rizea, Comput. Phys. Commun. 19, 23 (1980) http://dx.doi.org/10.1016/0010-4655(80)90062-4[Crossref]
  • [7] T. E. Simos, P. S. Williams, MATCH Communications in Mathematical and in Computer Chemistry 45, 123 (2002).
  • [8] J. D. Lambert, I. A. Watson, IMA J. Appl. Math. 18, 189 (1976). http://dx.doi.org/10.1093/imamat/18.2.189[Crossref]
  • [9] P. Henrici, Discrete variable methods in ordinary differential equations (John Wiley & Sons, New York, 1962)
  • [10] L. G. Ixaru, G. V. Berghe, Exponential fitting (Kluwer Academic Publisher, The Netherlands, 2004)
  • [11] L. G. Ixaru, M. Rizea, Comput. Phys. Commun. 38, 329 (1985) http://dx.doi.org/10.1016/0010-4655(85)90100-6[Crossref]
  • [12] A. Paris, L. Randez, IMA J. Appl. Math. 234, 767 (2010)
  • [13] M. Calvo, J. M. Franco, J. I. Montijano, L. Randez, IMA J. Appl. Math. 223, 387 (2009)
  • [14] T. E. Simos, Int. J. Mod. Phys. C 18, 315 (2007) http://dx.doi.org/10.1142/S0129183107009261[Crossref]
  • [15] Z. Wang, Comput. Phys. Commun. 171, 162 (2005) http://dx.doi.org/10.1016/j.cpc.2005.05.004[Crossref]
  • [16] A. Konguetsof, T. E. Simos, IMA J. Appl. Math. 158, 93 (2003)
  • [17] R. D'Ambrosio, E. Esposito, B. Paternoster, IMA J. Appl. Math. 235, 4888 (2011)
  • [18] R. D'Ambrosio, M. Ferro, B. Paternoster, Math. Comput. Simulat. 81, 1068 (2011) http://dx.doi.org/10.1016/j.matcom.2010.10.011[Crossref]
  • [19] Z. A. Anastassi, T. E. Simos, Phys. Rep. 482–483, 1 (2009) http://dx.doi.org/10.1016/j.physrep.2009.07.005[Crossref]
  • [20] T. Lyche, Numer. Math. 19, 65 (1972) http://dx.doi.org/10.1007/BF01395931[Crossref]
  • [21] J. P. Coleman, L. G. Ixaru, IMA J. Numer. Anal. 16, 179 (1996) http://dx.doi.org/10.1093/imanum/16.2.179[Crossref]
  • [22] J. R. Dormand, P. J. Prince, Comput. Math. Appl. 14, 1007 (1988)
  • [23] J. R. Dormand, M. E. A. IMA J. Numer. Anal. 7, 235 (1987) http://dx.doi.org/10.1093/imanum/7.2.235[Crossref]
  • [24] J. R. Dormand, M. E. A. IMA J. Numer. Anal. 7, 423 (1987) http://dx.doi.org/10.1093/imanum/7.4.423[Crossref]
  • [25] G. A. Panopoulos, Z. A. Anastassi, T. E. Simos, J. Math. Chem. 46, 604 (2009) http://dx.doi.org/10.1007/s10910-008-9506-0[Crossref]
  • [26] H. Van de Vyver, New Astronomy 10, 261 (2005) http://dx.doi.org/10.1016/j.newast.2004.12.004[Crossref]
  • [27] M. Calvo, J. M. Franco, J. I. Montijano, L. Randez, Comput. Phys. Commun. 181, 2044 (2010) http://dx.doi.org/10.1016/j.cpc.2010.08.019[Crossref]
  • [28] T. E. Simos, J. Chem. Phys. 133, 104108 (2010) http://dx.doi.org/10.1063/1.3488640[Crossref]
  • [29] I. Alolyan, T. E. Simos, J. Math. Chem. 48, 925 (2010) http://dx.doi.org/10.1007/s10910-010-9718-y[Crossref]
  • [30] I. Alolyan, T. Simos, J. Math. Chem. 48, 1092 (2010) http://dx.doi.org/10.1007/s10910-010-9728-9[Crossref]
  • [31] R. D'Ambrosio, L. G. Ixaru, B. Paternoster, Comput. Phys. Commun. 182, 322 (2011) http://dx.doi.org/10.1016/j.cpc.2010.10.009[Crossref]
  • [32] T. E. Simos, Acta Appl. Math. 110, 1331 (2010) http://dx.doi.org/10.1007/s10440-009-9513-6[Crossref]

Document Type

Publication order reference

Identifiers

YADDA identifier

bwmeta1.element.-psjd-doi-10_2478_s11534-011-0074-8
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