Zero Dispersion and Zero Dissipation Implicit Runge-Kutta Methods for the Numerical Solution of Oscillating IVPs
Provides specialized numerical methods for oscillatory IVPs, offering better accuracy for problems like the Schrödinger equation, though the improvement is incremental over existing Gauss methods.
The paper introduces two new implicit Runge-Kutta methods with zero dispersion and zero dissipation properties for solving oscillatory initial value problems, demonstrating improved efficiency on the radial Schrödinger equation and other test problems.
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 Schrödinger equation and other well known initial value problems.