A nonlinear optimization approach to the construction of general linear methods of high order
type: Item
instance of: scholarly article
title: A nonlinear optimization approach to the construction of general linear methods of high order
zbMATH Open document ID: 0879.65051
DOI: 10.1016/S0377-0427(97)00039-3
published in: Journal of Computational and Applied Mathematics
publication date: 1997-12-11T00:00:00Z
review text: The construction of diagonally implicit multistage integration methods of order and stage order \(p=q=7\) and \(p=q=8\) is presented. Both type 1 (explicit) and type 2 (implicit) methods are obtained. The construction is based on the variable-model trust-region least-squares algorithms.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
zbMATH DE Number: 1043281
zbMATH Keywords: general linear methods
zbMATH Keywords: A-stability
zbMATH Keywords: L-stability
zbMATH Keywords: least-squares minimization
zbMATH Keywords: diagonally implicit multistage integration methods
author: J. C. Butcher
author: Zdzislaw Jackiewicz
author: Hans D. Mittelmann
reviewed by: T. E. Simos
describes a project that uses: ADIFOR
describes a project that uses: nlr
describes a project that uses: NL2SOL
describes a project that uses: RODAS
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: Nordsieck representation of DIMSIMs
cites work: Generalized Padé approximations to the exponential function
cites work: Diagonally implicit general linear methods for ordinary differential equations
cites work: Construction of diagonally implicit general linear methods of type 1 and 2 for ordinary differential equations
cites work: Implementation of Diagonally Implicit Multistage Integration Methods for Ordinary Differential Equations
cites work: Construction of high order diagonally implicit multistage integration methods for ordinary differential equations
cites work: An Adaptive Nonlinear Least-Squares Algorithm
cites work: Q3702408
cites work: Q3313211
cites work: Solving Ordinary Differential Equations I
cites work: Q4714145
cites work: Variable stepsize diagonally implicit multistage integration methods for ordinary differential equations
cites work: Q5674335
cites work: Q4148902
cites work: Self-Scaling Variable Metric Algorithms without Line Search for Unconstrained Minimization
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description: scientific article; zbMATH DE number 1043281