Zero Dispersion and Zero Dissipation Implicit Runge-Kutta Methods for the Numerical Solution of Oscillating IVPs

TL;DR

This paper introduces two new implicit Runge-Kutta methods with zero dispersion and dissipation properties, improving the numerical solution of oscillating initial value problems like the radial Schrödinger equation.

Contribution

The paper presents novel implicit Runge-Kutta methods based on Gauss methods with zero dispersion and dissipation for better oscillatory IVP solutions.

Findings

Enhanced accuracy in oscillatory IVPs

Effective for radial Schrödinger equation

Zero dispersion and dissipation properties

Abstract

In this paper we present two new methods based on an implicit Runge-Kutta method Gauss which is of algebraic order fourth and has two stages: the first one has zero dispersion and the second one has zero dispersion and zero dissipation. The efficiency of these methods is measured while integrating the radial Schr\"odinger equation and other well known initial value problems.