Explicit two-derivative Runge–Kutta methods coupled with Richardson extrapolation

M. Eghbaljoo, G. Hojjati, A. Abdi, P. Khakzad

Statistics and Computer Science, University of Tabriz, Tabriz, Iran

Abstract: The aim of this paper is to derive efficient numerical algorithms for the numerical solution of nonstiff ordinary differential equations by applying the Richardson extrapolation technique to a class of explicit two-derivative Runge–Kutta methods. Theoretical results illustrate that the application of this technique has considerable impact on the accuracy and stability properties of the underlying numerical methods. The achieved improvements of the proposed algorithms are also confirmed by the results of some numerical experiments.

Key words: ordinary differential equations, second derivative methods, Runge–Kutta methods, Richardson extrapolation, stability properties, accuracy.

MSC: 65L05

Received: 14.12.2024
Revised: 07.02.2025
Accepted: 16.06.2025

DOI: 10.15372/SJNM20250406