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Journal of Mathematical Chemistry

, Volume 49, Issue 3, pp 711–764 | Cite as

A family of eight-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation

  • Ibraheem Alolyan
  • T. E. Simos
Original Paper

Abstract

A family of tenth algebraic order eight-step methods is constructed in this paper. For this family of methods, we require the phase-lag and its first, second and third derivatives to be vanished. Three alternative methods are proposed which satisfy the above requirements. An error analysis and a stability analysis is also investigated in this paper and a comparison with other methods is also studied. The new proposed methods are applied for the numerical solution of the one dimensional Schrödinger equation. The efficiency of the new methodology is proved via theoretical analysis and numerical applications.

Keywords

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

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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

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

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