Blended block BVMs (B\(_3\)VMs): A family of economical implicit methods for ODEs
type: Item
instance of: scholarly article
title: Blended block BVMs (B\(_3\)VMs): A family of economical implicit methods for ODEs
zbMATH Open document ID: 0982.65084
DOI: 10.1016/S0377-0427(99)00280-0
author: Luigi Brugnano
published in: Journal of Computational and Applied Mathematics
publication date: 2002-03-26T00:00:00Z
review text: The so called blended linear multistep methods were introduced by \textit{R. D. Skeel} and \textit{A. K. Kong} [ACM Trans. Math. Softw. 3, 326-345 (1977; Zbl 0399.65045)] as a means to circumvent the stability barriers of standard linear multistep formulas for the numerical solution of stiff initial value problems. In the paper under consideration this idea is translated to the so called boundary value methods in order to derive methods with a cheap implementation as well as good stability properties. The paper is organized as follows: In section 2 the relevant properties of block boundary value methods are briefly reviewed. Section 3 introduces the blended methods and studies some families of them. Finally, in the last section, some numerical experiments are presented to compare the behaviour of the new methods with the block boundary value methods used in the generalized Adams methods of \textit{F. Iavernaro} and \textit{F. Mazzia} [Appl. Numer. Math. 28, No. 2-4, 107-126 (1998; Zbl 0926.65076)].
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L05
zbMATH DE Number: 1437652
zbMATH Keywords: stiff systems
zbMATH Keywords: initial value problems
zbMATH Keywords: blended linear multistep methods
zbMATH Keywords: stability barriers
zbMATH Keywords: boundary value methods
zbMATH Keywords: numerical experiments
zbMATH Keywords: generalized Adams methods
reviewed by: Manuel Calvo
describes a project that uses: ParalleloGAM
describes a project that uses: RODAS
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1437652