A note on unconditionally stable linear multistep methods

Olof B. Widlund

Research output: Contribution to journalArticle

Abstract

It has been shown by Dahlquist [3] that the trapezoidal formula has the smallest truncation error among all linear multistep methods with a certain stability property. It is the purpose of this note to show that a slightly different stability requirement permits methods of higher accuracy.

Original languageEnglish (US)
Pages (from-to)65-70
Number of pages6
JournalBIT
Volume7
Issue number1
DOIs
StatePublished - Mar 1967

Fingerprint

Linear multistep Methods
Unconditionally Stable
Truncation Error
High Accuracy
Requirements

Keywords

  • Differential equations
  • multistep methods
  • stability

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics
  • Software
  • Computer Graphics and Computer-Aided Design

Cite this

A note on unconditionally stable linear multistep methods. / Widlund, Olof B.

In: BIT, Vol. 7, No. 1, 03.1967, p. 65-70.

Research output: Contribution to journalArticle

Widlund, Olof B. / A note on unconditionally stable linear multistep methods. In: BIT. 1967 ; Vol. 7, No. 1. pp. 65-70.
@article{031b627b7525453b985b4dd920df5640,
title = "A note on unconditionally stable linear multistep methods",
abstract = "It has been shown by Dahlquist [3] that the trapezoidal formula has the smallest truncation error among all linear multistep methods with a certain stability property. It is the purpose of this note to show that a slightly different stability requirement permits methods of higher accuracy.",
keywords = "Differential equations, multistep methods, stability",
author = "Widlund, {Olof B.}",
year = "1967",
month = "3",
doi = "10.1007/BF01934126",
language = "English (US)",
volume = "7",
pages = "65--70",
journal = "BIT Numerical Mathematics",
issn = "0006-3835",
publisher = "Springer Netherlands",
number = "1",

}

TY - JOUR

T1 - A note on unconditionally stable linear multistep methods

AU - Widlund, Olof B.

PY - 1967/3

Y1 - 1967/3

N2 - It has been shown by Dahlquist [3] that the trapezoidal formula has the smallest truncation error among all linear multistep methods with a certain stability property. It is the purpose of this note to show that a slightly different stability requirement permits methods of higher accuracy.

AB - It has been shown by Dahlquist [3] that the trapezoidal formula has the smallest truncation error among all linear multistep methods with a certain stability property. It is the purpose of this note to show that a slightly different stability requirement permits methods of higher accuracy.

KW - Differential equations

KW - multistep methods

KW - stability

UR - http://www.scopus.com/inward/record.url?scp=0009419915&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0009419915&partnerID=8YFLogxK

U2 - 10.1007/BF01934126

DO - 10.1007/BF01934126

M3 - Article

VL - 7

SP - 65

EP - 70

JO - BIT Numerical Mathematics

JF - BIT Numerical Mathematics

SN - 0006-3835

IS - 1

ER -