High-order schemes for conservative or dissipative systems
type: Item
instance of: scholarly article
title: High-order schemes for conservative or dissipative systems
zbMATH Open document ID: 1019.65042
DOI: 10.1016/S0377-0427(02)00713-6
author: Takayasu Matsuo
published in: Journal of Computational and Applied Mathematics
publication date: 2003-05-19T00:00:00Z
review text: The author presents a new approach to the design of finite difference methods. The paper focuses on the need to develop discrete schemes for solving conservative or dissipative initial value problems such as Hamiltonian systems without damping. The author begins by presenting (as Scheme 1) a first or second order finite difference scheme. In Scheme 2 he provides a general \(p\)-th order scheme which requires starting values in addition to the initial values. The order of the scheme is proved as its property to preserve the conservative or dissipative nature of the underlying problem. The paper concludes with some numerical examples and the author draws attention to the attractive feature that computational costs do not rise with the order of acuracy.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65P10
Mathematics Subject Classification ID: 37M15
Mathematics Subject Classification ID: 65L12
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 1912275
zbMATH Keywords: finite difference method
zbMATH Keywords: energy conservation
zbMATH Keywords: backward difference formulae
zbMATH Keywords: initial value problem
zbMATH Keywords: Hamiltonian systems
zbMATH Keywords: numerical examples
reviewed by: Neville J. Ford
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1912275