An optimized explicit Runge-Kutta method with increased phase-lag order for the numerical solution of the Schrödinger equation and related problems

摘要

In this paper 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. Keywords Numerical solution - Initial value problems (IVPs) - Explicit methods - Runge-Kutta methods - Schrödinger equation T. E. Simos is an active member of the European academy of sciences and arts, active member of the European academy of sciences.