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Journal of Mathematical Chemistry

, Volume 50, Issue 9, pp 2351–2373 | Cite as

A new high order two-step method with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation

  • Ibraheem Alolyan
  • T. E. Simos
Original Paper

Abstract

In this paper we develop a new hybrid method of high order with phase-lag and its first, second and third derivatives equal to zero. For the produced method we study its error and stability. We apply the newly obtained method to the Schrödinger equation. The application shows the efficiency of the new produced method.

Keywords

Numerical solution Schrödinger equation Multistep methods Hybrid methods Interval of periodicity P-stability Phase-lag Phase-fitted Derivatives of the phase-lag 

Mathematics Subject Classification

65L05 

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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  1. 1.Chair of Actuarial and Applied Mathematics, Department of Mathematics, College of SciencesKing Saud UniversityRiyadhSaudi Arabia
  2. 2.Department of Mathematics, College of SciencesKing Saud UniversityRiyadhSaudi Arabia
  3. 3.Laboratory of Computational Sciences, Department of Computer Science and Technology, Faculty of Sciences and TechnologyUniversity of PeloponneseTripolisGreece
  4. 4.AthensGreece

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