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Abstract <p>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 application of this technique has considerable impact on the accuracy and stability properties of the underlying numerical methods. The achieved improvements for the proposed algorithms are also confirmed by the results of some numerical experiments.</p>

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Explicit Two-Derivative Runge–Kutta Methods Coupled with the Richardson Extrapolation

  • 期刊论文

  • 发表日期：

    2025年12月1日

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

摘要

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 application of this technique has considerable impact on the accuracy and stability properties of the underlying numerical methods. The achieved improvements for the proposed algorithms are also confirmed by the results of some numerical experiments.