Construction of Nordsieck Second Derivative General Linear Methods with Inherent Quadratic Stability

This paper describes the construction of second derivative general linear methods in Nordsieck form with stability properties determined by quadratic stability functions. This is achieved by imposing the so-called inherent quadratic stability conditions. After satisfying order and inherent quadratic...

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Published inMathematical modelling and analysis Vol. 22; no. 1; pp. 60 - 77
Main Authors Movahedinejad, Akram, Hojjati, Gholamreza, Abdi, Ali
Format Journal Article
LanguageEnglish
Published Taylor & Francis 02.01.2017
Vilnius Gediminas Technical University
Subjects
A- and L-stability
Derivatives
Derivatives (Mathematics)
inherent quadratic stability
Linear equations
Mathematical analysis
Mathematical models
Mathematical research
Nordsieck methods
Parameters
Quadratic functions
second derivative methods
Stability
stiff differential equations
Nordsieck methods
stiff differential equations
second derivative methods
A– and L–stability
inherent quadratic stability
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Summary:This paper describes the construction of second derivative general linear methods in Nordsieck form with stability properties determined by quadratic stability functions. This is achieved by imposing the so-called inherent quadratic stability conditions. After satisfying order and inherent quadratic stability conditions, the remaining free parameters are used to find the methods with L-stable property. Examples of methods with p = q = s = r − 1 up to order four are given.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 23
ISSN:1392-6292
1648-3510
DOI:10.3846/13926292.2017.1269024