Rational Approximation Method for Stiff Initial Value Problems

Artur Karimov, Denis Butusov, Valery Andreev and Erivelton G. Nepomuceno
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Artur Karimov: Youth Research Institute, St. Petersburg Electrotechnical University “LETI”, 5 Professora Popova St., 197376 Saint Petersburg, Russia
Denis Butusov: Youth Research Institute, St. Petersburg Electrotechnical University “LETI”, 5 Professora Popova St., 197376 Saint Petersburg, Russia
Valery Andreev: Department of Computer-Aided Design, St. Petersburg Electrotechnical University “LETI”, 5 Professora Popova St., 197376 Saint Petersburg, Russia
Erivelton G. Nepomuceno: Centre for Ocean Energy Research, Department of Electronic Engineering, Maynooth University, W23 F2H6 Maynooth, Ireland

Mathematics, 2021, vol. 9, issue 24, 1-17

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.

Keywords: rational approximation; numerical integration; stiff problem; variable step size; ODE; stiff systems (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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