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Computing

, Volume 45, Issue 2, pp 175–181 | Cite as

Numerov-type methods with minimal phase-lag for the numerical integration of the one-dimensional Schrödinger equation

  • T. E. Simos
  • A. D. Raptis
Short Communications

Abstract

Three Numerov-type methods with phase-lag of order eight and ten are developed for the numerical integration of the one-dimensional Schrödinger equation. One has a large interval of periodicity and the other two areP-stable. Extensive numerical testing on the resonance problem indicates that these new methods are generally more accurate than other previously developed finite difference methods for this problem.

AMS Subject Classification

65L05 

Key words

Schrödinger equation resonance problem phase-lag 

Methoden vom Numerovschen Typ mit minimaler Phasenverschiebung für die numerische Integration der eindimensionalen Schrödinger-Gleichung

Zusammenfassung

Es werden Methoden vom Numerovschen Typ mit Phasenverschiebung achter und zehnter Ordnung für die numerische Integration der eindimensionalen Schrödinger-Gleichung entwickelt. Eine davon hat ein großes Periodizitätsintervall, die anderen zwei sindP-stabil. Ausgedehnte numerische Tests am Resonanzproblem zeigen, daß diese neuen Methoden für dieses Problem genauer sind als frühere Methoden.

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Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • T. E. Simos
    • 1
  • A. D. Raptis
    • 1
  1. 1.Department of MathematicsNational Technical University of AthensZografou AthensGreece

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