Exponentially-fitted explicit Runge-Kutta methods
type: Item
instance of: scholarly article
title: Exponentially-fitted explicit Runge-Kutta methods
zbMATH Open document ID: 0948.65066
DOI: 10.1016/S0010-4655(99)00365-3
author: Tanja Van Hecke
author: G. Vanden Berghe
author: H. De Meyer
author: M. Van Daele
published in: Computer Physics Communications
publication date: 2000-04-10T00:00:00Z
review text: It is pointed out that explicit Runge-Kutta methods cannot integrate polynomial solutions of degree greater than 1 exactly, except in the case of quadrature problems. Considerations based on this observation lead to the design of a new exponentially-fitted method. The new method is compared with the method of \textit{T. E. Simos} [Appl. Math. Lett. 9, No. 6, 61-66 (1996; Zbl 0864.65052)] and, as for the Simos method, is superior in performance over a classical method for some oscillatory problems. For two further test problems, almost perfect accuracy is achieved by the new method. However, this is evidently because the method integrates problems with purely oscillatory solutions exactly.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 1394620
zbMATH Keywords: explicit Runge-Kutta methods
zbMATH Keywords: initial-value problems
zbMATH Keywords: oscillating solutions
zbMATH Keywords: exponential fitting
zbMATH Keywords: performance
zbMATH Keywords: numerical examples
reviewed by: J. C. Butcher
MaRDI profile type: Publication
full work available at URL: s0010-4655(99)00365-3
OpenAlex ID: W2034818758
description: scientific article; zbMATH DE number 1394620