A Family of Runge-Kutta Methods with Zero Phase-Lag and Derivatives for the Numerical Solution of the Schrödinger Equation and Related Problems

2008/11/15 by Anastassi, Z. A., Vlachos, D. S., Simos, T. E.
#65L05 #65L06 #81Q05 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.0811.2469

Abstract

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.

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