EXPLICIT NORDSIECK SECOND DERIVATIVE GENERAL LINEAR METHODS FOR ODES

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 stab...

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Bibliographic Details
Published inThe ANZIAM journal Vol. 64; no. 1; pp. 69 - 88
Main Authors RAMAZANI, P., ABDI, A., HOJJATI, G., MORADI, A.
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.01.2022
Subjects
Accuracy
Methods
Ordinary differential equations
Runge-Kutta method
Stability
65L05
inherent Runge–Kutta stability
Nordsieck methods
second derivative methods
inherent quadratic stability
general linear methods
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Summary: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.
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ISSN:1446-1811
1446-8735
DOI:10.1017/S1446181122000049