Numerical Stability and Performance of Semi-Explicit and Semi-Implicit Predictor–Corrector Methods

Loïc Beuken, Olivier Cheffert, Aleksandra Tutueva, Denis Butusov and Vincent Legat
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Loïc Beuken: Ecole Polytechnique de Louvain, Université Catholique de Louvain, 1348 Louvain-la-Neuve, Belgium
Olivier Cheffert: Ecole Polytechnique de Louvain, Université Catholique de Louvain, 1348 Louvain-la-Neuve, Belgium
Aleksandra Tutueva: Department of Computer-Aided Design, Saint Petersburg Electrotechnical University “LETI”, 197376 Saint Petersburg, Russia
Denis Butusov: Youth Research Institute, Saint Petersburg Electrotechnical University “LETI”, 197376 Saint Petersburg, Russia
Vincent Legat: Institute of Mechanics, Materials and Civil Engineering (IMMC), Université Catholique de Louvain, L4.05.02, 1348 Louvain-la-Neuve, Belgium

Mathematics, 2022, vol. 10, issue 12, 1-14

Abstract: Semi-implicit multistep methods are an efficient tool for solving large-scale ODE systems. This recently emerged technique is based on modified Adams–Bashforth–Moulton (ABM) methods. In this paper, we introduce new semi-explicit and semi-implicit predictor–corrector methods based on the backward differentiation formula and Adams–Bashforth methods. We provide a thorough study of the numerical stability and performance of new methods and compare their stability with semi-explicit and semi-implicit Adams–Bashforth–Moulton methods and their performance with conventional linear multistep methods: Adams–Bashforth, Adams–Moulton, and BDF. The numerical stability of the investigated methods was assessed by plotting stability regions and their performances were assessed by plotting error versus CPU time plots. The mathematical developments leading to the increase in numerical stability and performance are carefully reported. The obtained results show the potential superiority of semi-explicit and semi-implicit methods over conventional linear multistep algorithms.

Keywords: semi-explicit integration; semi-implicit integration; predictor–corrector method; Adams–Bashforth–Moulton method; ODE solver (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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