Exponentially fitted explicit Runge-Kutta-Nyström methods
type: Item
instance of: scholarly article
title: Exponentially fitted explicit Runge-Kutta-Nyström methods
zbMATH Open document ID: 1060.65073
author: J. M. Franco
published in: Journal of Computational and Applied Mathematics
publication date: 2004-08-16T00:00:00Z
review text: The author derives so-called exponentially fitted Runge-Kutta-Nyström (EFRKN) schemes to numerically solve the Cauchy problem: \[ y''=f(t,y),\quad t\in[t_0,T], \quad y(t_0)=y_0,\quad y'(t_0)=y_0'. \] The EFRKN schemes integrate exactly differential systems whose solutions can be expressed as linear combination of the functions \(\{ \exp(\lambda t)\), \(\exp (-\lambda t)\}\), \(\lambda\in\mathbb{C}\), or \(\{\sin(\omega t), \cos(\omega t)\}\) when \(\lambda=i\omega\), \(\omega\in\mathbb{R}\). The author constructs explicit EFRKN methods with two and three stages and algebraic orders 3 an 4. He also discusses the problem of step length control and carries out numerical experiments.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 2091367
zbMATH Keywords: oscillatory solutions
zbMATH Keywords: Cauchy problem
zbMATH Keywords: step length control
zbMATH Keywords: numerical experiments
zbMATH Keywords: exponential fitting
zbMATH Keywords: initial value problems
zbMATH Keywords: Runge-Kutta-Nyström methods
describes a project that uses: RODAS
MaRDI profile type: Publication
full work available at URL: j.cam.2003.09.042
OpenAlex ID: W2009437712
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DOI: 10.1016/J.CAM.2003.09.042
description: scientific article; zbMATH DE number 2091367