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A generator of hybrid symmetric four-step methods for the numerical solution of the Schrödinger equation. (English) Zbl 1027.65094
Summary: A generator of hybrid explicit four-step methods with minimal phase-lag is developed. The methods are of sixth algebraic order and have large intervals of periodicity. The coefficients of the methods are determined in order to have minimal phase-lag. The efficiency of the new methods is showed by their application to the Schrödinger equation and by their comparison with other well-known methods.

MSC:
65L06Multistep, Runge-Kutta, and extrapolation methods
65L20Stability and convergence of numerical methods for ODE
34L40Particular ordinary differential operators
34C25Periodic solutions of ODE
65L05Initial value problems for ODE (numerical methods)
34A34Nonlinear ODE and systems, general
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References:
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