Efficient General Linear Methods of High Order with Inherent Quadratic Stability

Michał Braś; Zdzislaw Jackiewicz

doi:10.3846/13926292.2014.955893

Efficient General Linear Methods of High Order with Inherent Quadratic Stability

Michał Braś, Zdzislaw Jackiewicz

Mathematical and Statistical Sciences, School of (SoMSS)

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Abstract: We search for general linear methods with s internal stages and r = s + 1 external stages of order p = s + 1 and stage order q = s. We require that stability function of these methods has only two non-zero roots. This is achieved by imposing the so-called inherent quadratic stability conditions. Examples of such general linear methods which are A- and L-stable up to the order p = 8 and stage order q = p - 1 are derived.

Original language	English (US)
Pages (from-to)	450-468
Number of pages	19
Journal	Mathematical Modelling and Analysis
Volume	19
Issue number	4
DOIs	https://doi.org/10.3846/13926292.2014.955893
State	Published - Jan 1 2014

Keywords

A- and L-stability
general linear methods
inherent quadratic stability
order and stage order

ASJC Scopus subject areas

Analysis
Modeling and Simulation

Access to Document

10.3846/13926292.2014.955893

Cite this

@article{bc058891db5f46df861666e5631ea589,

title = "Efficient General Linear Methods of High Order with Inherent Quadratic Stability",

abstract = "Abstract: We search for general linear methods with s internal stages and r = s + 1 external stages of order p = s + 1 and stage order q = s. We require that stability function of these methods has only two non-zero roots. This is achieved by imposing the so-called inherent quadratic stability conditions. Examples of such general linear methods which are A- and L-stable up to the order p = 8 and stage order q = p - 1 are derived.",

keywords = "A- and L-stability, general linear methods, inherent quadratic stability, order and stage order",

author = "Micha{\l} Bra{\'s} and Zdzislaw Jackiewicz",

note = "Funding Information: ∗ The work of Michal Bra´s was supported by the National Science Center under grant DEC-2011/01/N/ST1/02672 and by the Polish Ministry of Science and Higher Education. Publisher Copyright: {\textcopyright} 2014, {\textcopyright} Vilnius Gediminas Technical University, 2014.",

year = "2014",

month = jan,

day = "1",

doi = "10.3846/13926292.2014.955893",

language = "English (US)",

volume = "19",

pages = "450--468",

journal = "Mathematical Modelling and Analysis",

issn = "1392-6292",

publisher = "Vilnius Gediminas Technical University",

number = "4",

}

TY - JOUR

T1 - Efficient General Linear Methods of High Order with Inherent Quadratic Stability

AU - Braś, Michał

AU - Jackiewicz, Zdzislaw

N1 - Funding Information: ∗ The work of Michal Bra´s was supported by the National Science Center under grant DEC-2011/01/N/ST1/02672 and by the Polish Ministry of Science and Higher Education. Publisher Copyright: © 2014, © Vilnius Gediminas Technical University, 2014.

PY - 2014/1/1

Y1 - 2014/1/1

N2 - Abstract: We search for general linear methods with s internal stages and r = s + 1 external stages of order p = s + 1 and stage order q = s. We require that stability function of these methods has only two non-zero roots. This is achieved by imposing the so-called inherent quadratic stability conditions. Examples of such general linear methods which are A- and L-stable up to the order p = 8 and stage order q = p - 1 are derived.

AB - Abstract: We search for general linear methods with s internal stages and r = s + 1 external stages of order p = s + 1 and stage order q = s. We require that stability function of these methods has only two non-zero roots. This is achieved by imposing the so-called inherent quadratic stability conditions. Examples of such general linear methods which are A- and L-stable up to the order p = 8 and stage order q = p - 1 are derived.

KW - A- and L-stability

KW - general linear methods

KW - inherent quadratic stability

KW - order and stage order

UR - http://www.scopus.com/inward/record.url?scp=84934178364&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84934178364&partnerID=8YFLogxK

U2 - 10.3846/13926292.2014.955893

DO - 10.3846/13926292.2014.955893

M3 - Article

AN - SCOPUS:84934178364

SN - 1392-6292

VL - 19

SP - 450

EP - 468

JO - Mathematical Modelling and Analysis

JF - Mathematical Modelling and Analysis

IS - 4

ER -

Efficient General Linear Methods of High Order with Inherent Quadratic Stability

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this