Symmetric boundary value methods for second order initial and boundary value problems
type: Item
instance of: scholarly article
title: Symmetric boundary value methods for second order initial and boundary value problems
zbMATH Open document ID: 1117.65107
author: Pierluigi Amodio
author: Felice Iavernaro
published in: Mediterranean Journal of Mathematics
publication date: 2007-04-26T00:00:00Z
review text: This paper is concerned with the numerical solution of both initial and boundary value problems for special second order equations \(y^{\prime\prime}(t)= f(y(t))\) by means of the so called Boundary Value Methods proposed by \textit{L. Brugnano} and \textit{D. Trigiante} [Solving differential equations by multistep. Initial and boundary value methods. Stability and Control: Theory, Methods and Applications. 6. London: Gordon and Breach (1998; Zbl 0934.65074)]. Here only symmetric multistep methods \( \rho (E) y_{n+j}= h^2 \sigma (E) f_{n+j}\) have been considered and some results on the stability and conditioning of these methods derived from the study of the boundary loci \( D_1= \{ \rho (e^{i \theta} )/ \sigma (e^{i \theta}; \theta \in [0, \pi) \}\) and \( D_2= \{ \rho (e^{x} )/ \sigma (e^{x}; x \in [0, + \infty) \}\) have been obtained. Finally, some numerical experiments with the problems of Kepler and Troetsch are presented to show how BVM based on symmetric second order multistep methods can be used to deal with these problems.
reviewed by: Manuel Calvo
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L10
zbMATH DE Number: 5147137
zbMATH Keywords: Initial and boundary value problems
zbMATH Keywords: Linear multistep methods
zbMATH Keywords: Boundary value methods
MaRDI profile type: Publication
full work available at URL: s00009-006-0085-7
OpenAlex ID: W2088088757
DOI: 10.1007/S00009-006-0085-7
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description: scientific article; zbMATH DE number 5147137