One step integration methods with maximum stability regions
type: Item
instance of: scholarly article
title: One step integration methods with maximum stability regions
zbMATH Open document ID: 0539.65050
DOI: 10.1016/0378-4754(84)90039-9
author: Ingemar P. E. Kinnmark
author: William G. Gray
published in: Mathematics and Computers in Simulation
publication date: 1984-01-01T00:00:00Z
review text: For all \(K\in {\mathbb{N}}\) stability polynomials M(z) of one-step K-stage schemes are given which have the maximal stability interval K-1 on the imaginary axis. Moreover it is shown that for these polynomials one has \(M(i(K-1))=\exp(i(K-1)\pi /2).\) The schemes are of oder one or two only. For stability polynomials of order 3 or 4 and large stability intervals on the imaginary axis see the following review.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
zbMATH DE Number: 3858325
zbMATH Keywords: maximum stability regions
zbMATH Keywords: one step methods
zbMATH Keywords: optimal stability
zbMATH Keywords: Euler's method
zbMATH Keywords: Runge-Kutta methods
reviewed by: Rolf Jeltsch
MaRDI profile type: Publication
full work available at URL: 0378-4754(84)90039-9
OpenAlex ID: W1969251581
cites work: Q3661894
cites work: Explicit Runge-Kutta formulas with increased stability boundaries
cites work: Largest disk of stability of explicit Runge-Kutta methods
cites work: New stability theorems concerning one-step numerical methods for ordinary differential equations
description: scientific article; zbMATH DE number 3858325