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An efficient variable stepsize rational method for stiff, singular and singularly perturbed problemsopen access

Authors
Qureshi, SaniaSoomro, AmanullahHincal, EvrenLee, Jung RyePark, ChoonkilOsman, Mohammad Shahril
Issue Date
Dec-2022
Publisher
ELSEVIER
Keywords
Blow-up solutions; Single-step; Variable stepsize; Stability; Local truncation error; Stiffness
Citation
ALEXANDRIA ENGINEERING JOURNAL, v.61, no.12, pp.10953 - 10963
Indexed
SCIE
SCOPUS
Journal Title
ALEXANDRIA ENGINEERING JOURNAL
Volume
61
Number
12
Start Page
10953
End Page
10963
URI
https://scholarworks.bwise.kr/hanyang/handle/2021.sw.hanyang/169988
DOI
10.1016/j.aej.2022.03.014
ISSN
1110-0168
Abstract
In this article, a new iterative method of the rational type having fifth-order of accuracy is proposed to solve initial value problems. The method is self-starting, stable, consistent, and convergent, whereas local truncation error analysis has also been discussed. Furthermore, the method has been analyzed with a variable stepsize approach that increases performance while taking fewer steps with acceptable local errors. The method is also tested against some existing fifth-order methods having rational structure. The proposed one outperforms concerning maximum absolute error, final absolute error, average error, and norm, while CPU time computed in seconds is comparable. Furthermore, stiff, singular, and singularly perturbed problems for single and system of differential equations chosen for simulations yielded minor errors when solved with the new rational method.
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