A Family of Runge-Kutta Methods with Zero Phase-Lag and Derivatives for the Numerical Solution of the Schrödinger Equation and Related Problems
This work provides a more accurate numerical integration technique for scientists solving oscillatory problems in quantum mechanics and related fields.
The authors developed a family of explicit Runge-Kutta methods with zero phase-lag and its derivatives for solving the Schrödinger equation and oscillatory ODEs. Numerical results demonstrate the superiority of nullifying both phase-lag and its derivatives over existing methods.
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.