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Zbl 1217.65143
Alolyan, Ibraheem; Simos, T.E.
A family of eight-step methods with vanished phase-lag and its derivatives for the numerical integration of the Schrödinger equation. (English)
[J] J. Math. Chem. 49, No. 3, 711-764 (2011). ISSN 0259-9791; ISSN 1572-8897/e

Summary: 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.

MSC 2000:: *65L06 Multistep, Runge-Kutta, and extrapolation methods

Keywords: numerical solution; Schrödinger equation; multistep methods; hybrid methods; interval of periodicity; P-stability; phase-lag; phase-fitted

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