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A family of Runge-Kutta methods with zero phase-lag and derivatives for the numerical solution of the Schrödinger equation and related problems. (English) Zbl 1200.81045
Summary: We construct a family of two new optimized explicit Runge-Kutta methods with zero phase-lag and derivatives for the numerical solution of the time-independent radial Schrödinger equation and related ordinary differential equations with oscillating solutions. The numerical results show the superiority of the new technique of nullifying both the phase-lag and its derivatives.
MSC:
81Q05Closed and approximate solutions to quantum-mechanical equations
34L40Particular ordinary differential operators
81T80Simulation and numerical modelling (quantum field theory)
81-08Computational methods (quantum theory)
65L06Multistep, Runge-Kutta, and extrapolation methods
Software:
pythNon; SCHOL; VFGEN
References:
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