A trigonometrically fitted block method for solving oscillatory second-order initial value problems and Hamiltonian systems
type: Item
instance of: scholarly article
title: A trigonometrically fitted block method for solving oscillatory second-order initial value problems and Hamiltonian systems
zbMATH Open document ID: 1487.65086
DOI: 10.1155/2017/9293530
published in: International Journal of Differential Equations
publication date: 2018-08-10T00:00:00Z
review text: Summary: In this paper, we present a block hybrid trigonometrically fitted Runge-Kutta-Nyström method (BHTRKNM), whose coefficients are functions of the frequency and the step-size for directly solving general second-order initial value problems (IVPs), including Hamiltonian systems such as the energy conserving equations and systems arising from the semidiscretization of partial differential equations (PDEs). Four discrete hybrid formulas used to formulate the BHTRKNM are provided by a continuous one-step hybrid trigonometrically fitted method with an off-grid point. We implement BHTRKNM in a block-by-block fashion; in this way, the method does not suffer from the disadvantages of requiring starting values and predictors which are inherent in predictor-corrector methods. The stability property of the BHTRKNM is discussed and the performance of the method is demonstrated on some numerical examples to show accuracy and efficiency advantages.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 6915945
author: F. F. Ngwane
author: Samuel N. Jator
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/9293530
OpenAlex ID: W2579946039
Wikidata QID: Q59144310
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description: scientific article; zbMATH DE number 6915945