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

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 quadrati...

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Bibliographic Details
Main Authors: Akram Movahedinejad, Gholamreza Hojjati, Ali Abdi
Format: Article
Language:English
Published: Vilnius Gediminas Technical University 2017-01-01
Series:Mathematical Modelling and Analysis
Subjects:
stiff differential equations
second derivative methods
Nordsieck methods
inherent quadratic stability
A– and L–stability
Online Access:https://journals.vgtu.lt/index.php/MMA/article/view/874
Description
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.
ISSN:1392-6292
1648-3510

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