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

TL;DR

This paper introduces a new family of optimized explicit Runge-Kutta methods designed to improve the numerical solution of oscillatory differential equations like the Schrödinger equation by eliminating phase-lag and its derivatives.

Contribution

The paper develops and analyzes a novel family of Runge-Kutta methods with zero phase-lag and derivatives, enhancing accuracy for oscillatory problems.

Findings

Methods outperform existing techniques in accuracy.

Nullifying phase-lag and derivatives improves solution quality.

Numerical results confirm the effectiveness of the new methods.

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 Schr\"odinger 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.