Exploiting structure in the construction of DIMSIMs
type: Item
instance of: scholarly article
title: Exploiting structure in the construction of DIMSIMs
zbMATH Open document ID: 0937.65088
DOI: 10.1016/S0377-0427(99)00091-6
published in: Journal of Computational and Applied Mathematics
publication date: 1999-09-02T00:00:00Z
review text: This paper is concerned with the construction of \(s\)-stage, \(r\)-value diagonally implicit multivalue methods with \(r=s\) and stage order equal to the order of consistency and whose stability regions are exactly the same as certain Runge-Kutta methods of equivalent order. The structure of the nonlinear equations that define these methods is exploited to obtain high order (8) methods using a least squares minimization approach.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 1331027
zbMATH Keywords: diagonally implicit multivalue methods
zbMATH Keywords: consistency
zbMATH Keywords: stability regions
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: high order
zbMATH Keywords: least squares minimization
author: Zdzislaw Jackiewicz
author: Hans D. Mittelmann
reviewed by: Kevin Burrage
describes a project that uses: nlr
describes a project that uses: RODAS
describes a project that uses: NL2SOL
MaRDI profile type: Publication
cites work: Algorithm 717: Subroutines for maximum likelihood and quasi-likelihood estimation of parameters in nonlinear regression models
cites work: Diagonally-implicit multi-stage integration methods
cites work: A transformation for the analysis of DIMSIMs
cites work: Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations
cites work: Construction of high order diagonally implicit multistage integration methods for ordinary differential equations
cites work: A nonlinear optimization approach to the construction of general linear methods of high order
cites work: Q4868581
cites work: Q4714145
description: scientific article; zbMATH DE number 1331027