Conservation laws and the numerical solution of ODEs. II
type: Item
instance of: scholarly article
title: Conservation laws and the numerical solution of ODEs. II
zbMATH Open document ID: 0947.65086
DOI: 10.1016/S0898-1221(99)00183-2
publication date: 2000-01-20T00:00:00Z
review text: The author discusses practical aspects of applying his coordinate projection method to approximate the solution of ordinary differential equations with side conditions using multistep difference approximations with variable stepsize [cf. part I, ibid. Part B 12, 1287-1296 (1986; Zbl 0641.65057) and the author's book ``Numerical solution of ordinary differential equations'' (1994; Zbl 0832.65063), Chapter 5]. In the coordinate projection method the value \(y^*_n\) at the \(n\)th step of the solution of the unconstrained problem is projected onto the manifold spanned by the side conditions \(y_n= Py^*_n\) to produce a solution of the constrained problem. It is shown that an asymptotic estimate of the global error of the constrained problem is obtained as the projection of the asymptotic estimate of the unconstrained problem, a result obtained by \textit{E. Eich} for backward difference algorithms [SIAM J. Numer. Anal. 30, No. 5, 1467-1482 (1993; Zbl 0785.65079)]. Methods for coding Runge-Kutta algorithms and difficulties with stiff problems are discussed. Codes have been written for introduction of side conditions into ordinary differential problem solvers from the MATLAB ODE Suite. These are ODE 23, ODE 45, ODE 113, ODE 15s. Results of numerical experiments with ODE 45 and ODE 113 are present.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L50
zbMATH DE Number: 1391609
zbMATH Keywords: error bound
zbMATH Keywords: coordinate projection method
zbMATH Keywords: side conditions
zbMATH Keywords: multistep difference approximations
zbMATH Keywords: variable stepsize
zbMATH Keywords: Runge-Kutta algorithms
zbMATH Keywords: stiff problems
zbMATH Keywords: numerical experiments
author: L. F. Shampine
reviewed by: John B. Butler jun.
describes a project that uses: Matlab
describes a project that uses: Ode15s
describes a project that uses: ode113
describes a project that uses: MATLAB ODE suite
describes a project that uses: ode23
describes a project that uses: ode45
describes a project that uses: ode23s
MaRDI profile type: Publication
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full work available at URL: s0898-1221(99)00183-2
OpenAlex ID: W1988018377
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 1391609