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Zbl 0985.65083
Simos, T.E.
An embedded Runge-Kutta method with phase-lag of order infinity for the numerical solution of the Schrödinger equation. (English)
[J] Int. J. Mod. Phys. C 11, No.6, 1115-1133 (2000). ISSN 0129-1831

Based on a test equation Runge-Kutta methods of five and four algebraic orders are constructed characterized by total phase fitting (or phase-lag of order infinity) by the solution of a dispersion relation. The methods are applied to the one-dimensional (radial) Schrödinger equation in the forms of bound-states and the resonance problems as well as to coupled differential equations of Schrödinger type, and compared to other contemporary numerical methods. The efficiency of the proposed technique is documented.
[M.Gousidou-Koutita (Thessaloniki)]

MSC 2000:: *65L06 Multistep, Runge-Kutta, and extrapolation methods
65L05 Initial value problems for ODE (numerical methods)
34L40 Particular ordinary differential operators
34A34 Nonlinear ODE and systems, general

Keywords: radial Schrödinger equation; Runge-Kutta methods; phase fitting; phase-lag; resonance

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Zentralblatt MATH Berlin [Germany]