Karimov, Artur and Butusov, Denis and Andreev, Valery and Nepomuceno, Erivelton (2021) Rational Approximation Method for Stiff Initial Value Problems. Mathematics, 9 (24). p. 3185. ISSN 2227-7390

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Abstract

While purely numerical methods for solving ordinary differential equations (ODE), e.g., Runge–Kutta methods, are easy to implement, solvers that utilize analytical derivations of the right-hand side of the ODE, such as the Taylor series method, outperform them in many cases. Nevertheless, the Taylor series method is not well-suited for stiff problems since it is explicit and not A-stable. In our paper, we present a numerical-analytical method based on the rational approximation of the ODE solution, which is naturally A- and A(α)-stable. We describe the rational approximation method and consider issues of order, stability, and adaptive step control. Finally, through examples, we prove the superior performance of the rational approximation method when solving highly stiff problems, comparing it with the Taylor series and Runge–Kutta methods of the same accuracy order.

Item Type:	Article
Keywords:	rational approximation; numerical integration; stiff problem; variable step size; ODE; stiff systems;
Academic Unit:	Faculty of Science and Engineering > Electronic Engineering Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	16843
Identification Number:	https://doi.org/10.3390/math9243185
Depositing User:	Erivelton Nepomuceno
Date Deposited:	11 Jan 2023 12:18
Journal or Publication Title:	Mathematics
Publisher:	MDPI
Refereed:	Yes
URI:	Publisher
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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