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An optimized explicit Runge-Kutta method with increased phase-lag order for the numerical solution of the Schrödinger equation and related problems. (English) Zbl 1200.81052
Summary: We present an optimized explicit Runge-Kutta method, which is based on a method of Fehlberg with six stages and fifth algebraic order and has improved characteristics of the phase-lag error. We measure the efficiency of the new method in comparison to other numerical methods, through the integration of the Schrödinger equation and three other initial value problems.
MSC:
81Q05Closed and approximate solutions to quantum-mechanical equations
81T80Simulation and numerical modelling (quantum field theory)
81-08Computational methods (quantum theory)
34L40Particular ordinary differential operators
65L06Multistep, Runge-Kutta, and extrapolation methods
References:
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