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Zbl 1202.81027
Alolyan, Ibraheem; Simos, T.E.
High algebraic order methods with vanished phase-lag and its first derivative for the numerical solution of the Schrödinger equation. (English)
[J] J. Math. Chem. 48, No. 4, 925-958 (2010). ISSN 0259-9791; ISSN 1572-8897/e

Summary: In the present paper we develop a high algebraic order multistep method. The characteristic property of the new proposed method is the requirement of vanishing the phase-lag and its derivatives. The new method is applied for the approximate solution of the radial Schrödinger equation. The efficiency of the new methodology is proved via error analysis and numerical applications.

MSC 2000:: *81Q05 Closed and approximate solutions to quantum-mechanical equations
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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Zentralblatt MATH Berlin [Germany]