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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:

65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
34L40 Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.)
34C25 Periodic solutions to ordinary differential equations
65L05 Numerical methods for initial value problems involving ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
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