Explicit finite-difference methods for nonlinear dynamic systems: Froude's pendulum
type: Item
instance of: scholarly article
title: Explicit finite-difference methods for nonlinear dynamic systems: Froude's pendulum
zbMATH Open document ID: 0900.70011
DOI: 10.1016/0045-7825(95)00952-3
author: J. Ning
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 1998-08-27T00:00:00Z
review text: Numerical schemes based on first-order methods and a second-order method are developed and analysed for solving the nonlinear Froude's pendulum system. The second-order method is developed by taking a linear combination of three first-order methods. Though implicit in nature, with the resulting improvements in stability, the methods are applied explicitly. These methods are extended to a more general second-order ordinary differential equation. Stability of the numerical methods is approached from the point of view of dynamical systems. lt is found that the methods are stable under the same conditions as those required by the linearized schemes in the neighbourhood of constant, stable, fixed points of the underlying initial-value problem. For the second-order method, this result is found to hold for any chosen value of the step-length.
Mathematics Subject Classification ID: 70-08
Mathematics Subject Classification ID: 70K40
Mathematics Subject Classification ID: 65L12
zbMATH DE Number: 1087156
zbMATH Keywords: linear combination of three first-order methods
zbMATH Keywords: stability
MaRDI profile type: Publication
full work available at URL: 0045-7825(95)00952-3
OpenAlex ID: W2029460028
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description: scientific article; zbMATH DE number 1087156