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

2008/11/15 by N. G. Tselios, Tselios, N. G., Zacharias Anastassi +3
Engineering · Mathematics · #65L05 #65L06 #81Q05 #Computational Fluid Dynamics and Aerodynamics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.0811.2480

openalex publication_date 2008/11/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Schrödinger equation and other well known initial value problems.

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