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EXPLICIT NORDSIECK SECOND DERIVATIVE GENERAL LINEAR METHODS FOR ODES

Part of: Numerical analysis: Ordinary differential equations

Published online by Cambridge University Press:  25 April 2022

P. RAMAZANI Open the ORCID record for P. RAMAZANI [Opens in a new window] ,
A. ABDI Open the ORCID record for A. ABDI [Opens in a new window] ,
G. HOJJATI Open the ORCID record for G. HOJJATI [Opens in a new window]  and
A. MORADI Open the ORCID record for A. MORADI [Opens in a new window]
P. RAMAZANI
Affiliation:
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran; e-mail: p.ramazanii@tabrizu.ac.ir, ghojjati@tabrizu.ac.ir, a_moradi@tabrizu.ac.ir
A. ABDI*
Affiliation:
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran; e-mail: p.ramazanii@tabrizu.ac.ir, ghojjati@tabrizu.ac.ir, a_moradi@tabrizu.ac.ir
G. HOJJATI
Affiliation:
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran; e-mail: p.ramazanii@tabrizu.ac.ir, ghojjati@tabrizu.ac.ir, a_moradi@tabrizu.ac.ir
A. MORADI
Affiliation:
Faculty of Mathematical Sciences, University of Tabriz, Tabriz, Iran; e-mail: p.ramazanii@tabrizu.ac.ir, ghojjati@tabrizu.ac.ir, a_moradi@tabrizu.ac.ir
*
e-mail: a_abdi@tabrizu.ac.ir
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Abstract

The paper deals with the construction of explicit Nordsieck second derivative general linear methods with s stages of order p with $p=s$ and high stage order $q=p$ with inherent Runge–Kutta or quadratic stability properties. Satisfying the order and stage order conditions together with inherent stability conditions leads to methods with some free parameters, which will be used to obtain methods with a large region of absolute stability. Examples of methods with r external stages and $p=q=s=r-1$ up to order five are given, and numerical experiments in a fixed stepsize environment are presented.

Keywords

Nordsieck methodssecond derivative methodsgeneral linear methodsinherent Runge–Kutta stabilityinherent quadratic stability

MSC classification

Primary: 65L05: Initial value problems
Type
Research Article
Information
The ANZIAM Journal , Volume 64 , Issue 1 , January 2022 , pp. 69 - 88
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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