A variable parameter embedded DIRK algorithm for the numerical integration of stiff systems of ODEs
type: Item
instance of: scholarly article
title: A variable parameter embedded DIRK algorithm for the numerical integration of stiff systems of ODEs
zbMATH Open document ID: 0623.65076
DOI: 10.1016/0898-1221(87)90005-8
author: A. H. Al-Rabeh
publication date: 1987-01-01T00:00:00Z
review text: The defining matrix of a single diagonally implicit Runge-Kutta (SDIRK) method has a single eigenvalue, \(\gamma\), of multiplicity s. This admits an efficient implementation as each step requires the solution of s systems of linear equations with the same matrix (I-h\(\gamma\) J) where J is a Jacobian matrix. For problems in which the change in J is slight, choosing a constant step h allows preservation of both the matrix and its LU-factorization. The author proposes that the step length may be allowed to change while maintaining \(h\gamma\) constant. This would tend to maintain efficiency in implementation. Unfortunately, constraints on \(\gamma\) to maintain order and A-stability precludes an unrestricted choice. Results from an (unclear) implementation on four standard problems suggest some improvement in efficiency is possible for some problems.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 4011817
zbMATH Keywords: efficient implicit methods
zbMATH Keywords: DIRK
zbMATH Keywords: singly diagonally implicit Runge-Kutta method
zbMATH Keywords: LU-factorization
zbMATH Keywords: A-stability
MaRDI profile type: Publication
full work available at URL: 0898-1221(87)90005-8
OpenAlex ID: W1992424415
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published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 4011817