Semi-Implicit Multistep Extrapolation ODE Solvers

Denis Butusov, Aleksandra Tutueva, Petr Fedoseev, Artem Terentev and Artur Karimov
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Denis Butusov: Youth Research Institute, Saint Petersburg Electrotechnical University “LETI”, 197376 Saint Petersburg, Russia
Aleksandra Tutueva: Department of Computer-Aided Design, Saint Petersburg Electrotechnical University “LETI”, 197376 Saint Petersburg, Russia
Petr Fedoseev: Department of Computer-Aided Design, Saint Petersburg Electrotechnical University “LETI”, 197376 Saint Petersburg, Russia
Artem Terentev: Department of Computer-Aided Design, Saint Petersburg Electrotechnical University “LETI”, 197376 Saint Petersburg, Russia
Artur Karimov: Youth Research Institute, Saint Petersburg Electrotechnical University “LETI”, 197376 Saint Petersburg, Russia

Mathematics, 2020, vol. 8, issue 6, 1-18

Abstract: Multistep methods for the numerical solution of ordinary differential equations are an important class of applied mathematical techniques. This paper is motivated by recently reported advances in semi-implicit numerical integration methods, multistep and extrapolation solvers. Here we propose a novel type of multistep extrapolation method for solving ODEs based on the semi-implicit basic method of order 2. Considering several chaotic systems and van der Pol nonlinear oscillator as examples, we implemented a performance analysis of the proposed technique in comparison with well-known multistep methods: Adams–Bashforth, Adams–Moulton and the backward differentiation formula. We explicitly show that the multistep semi-implicit methods can outperform the classical linear multistep methods, providing more precision in the solutions for nonlinear differential equations. The analysis of stability regions reveals that the proposed methods are more stable than explicit linear multistep methods. The possible applications of the developed ODE solver are the long-term simulations of chaotic systems and processes, solving moderately stiff differential equations and advanced modeling systems.

Keywords: numerical integration; multistep methods; semi-implicit methods; chaotic systems; extrapolation; ODE solver (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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