An explicit four-step phase-fitted method for the numerical integration of second-order initial-value problems
type: Item
instance of: scholarly article
title: An explicit four-step phase-fitted method for the numerical integration of second-order initial-value problems
zbMATH Open document ID: 0823.65067
DOI: 10.1016/0377-0427(94)90015-9
published in: Journal of Computational and Applied Mathematics
publication date: 1995-07-05T00:00:00Z
review text: This paper is concerned with the numerical solution of initial value problems for special second-order equations i.e. \(y'' = f(x,y)\), by means of linear multistep methods. A family of four-step explicit methods with a free parameter and local truncation error of order six is presented. It is shown that by choosing appropriately the free parameter it is possible to get a method which has a phase-lag of infinite order and an interval of periodicity \((0, H^ 2_ 0)\) with \(H_ 0 \cong 4.40\). This means that for the linear test equation \(y'' + k^ 2 y = 0\) and a fixed stepsize \(h\) such that \(0 < hk < H_ 0\) the numerical method exhibits the same periodic behaviour as the exact solution. Finally, the numerical experiments obtained with four test problems are presented to confirm the expected behaviour of the method.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 758523
zbMATH Keywords: explicit four-step phase fitted method
zbMATH Keywords: second-order initial-value problems
zbMATH Keywords: linear multistep methods
zbMATH Keywords: numerical experiments
zbMATH Keywords: test problems
author: T. E. Simos
reviewed by: Manuel Calvo
MaRDI profile type: Publication
full work available at URL: 0377-0427(94)90015-9
OpenAlex ID: W2054361022
cites work: A one-step method for direct integration of structural dynamic equations
cites work: Q3283176
cites work: A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems
cites work: A Noumerov-type method with minimal phase-lag for the integration of second order periodic initial-value problems. II: Explicit method
cites work: An explicit sixth-order method with phase-lag of order eight for \(y''=f(t,y)\)
cites work: Two-step fourth-order \(P\)-stable methods with phase-lag of order six for \(y''=f(t,y)\)
cites work: Numerical Methods for y″ =f(x, y) via Rational Approximations for the Cosine
cites work: An Improved Eigenvalue Corrector Formula for Solving the Schrodinger Equation for Central Fields
cites work: High-order P-stable multistep methods
cites work: Efficient Integration Methods for Stiff Systems of Ordinary Differential Equations
cites work: Two-step methods for the numerical solution of the Schrödinger equation
cites work: A four-step phase-fitted method for the numerical integration of second order initial-value problems
cites work: Numerov-type methods with minimal phase-lag for the numerical integration of the one-dimensional Schrödinger equation
cites work: Phase properties of high order, almost P-stable formulae
cites work: Predictor-Corrector Methods for Periodic Second-Order Initial-Value Problems
cites work: On the numerical integration of second-order initial value problems with a periodic forcing function
cites work: Stabilization of Cowell's classical finite difference method for numerical integration
description: scientific article; zbMATH DE number 758523