Stability Analysis and Optimization of Semi-Explicit Predictor–Corrector Methods

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

Mathematics, 2021, vol. 9, issue 19, 1-16

Abstract: The increasing complexity of advanced devices and systems increases the scale of mathematical models used in computer simulations. Multiparametric analysis and study on long-term time intervals of large-scale systems are computationally expensive. Therefore, efficient numerical methods are required to reduce time costs. Recently, semi-explicit and semi-implicit Adams–Bashforth–Moulton methods have been proposed, showing great computational efficiency in low-dimensional systems simulation. In this study, we examine the numerical stability of these methods by plotting stability regions. We explicitly show that semi-explicit methods possess higher numerical stability than the conventional predictor–corrector algorithms. The second contribution of the reported research is a novel algorithm to generate an optimized finite-difference scheme of semi-explicit and semi-implicit Adams–Bashforth–Moulton methods without redundant computation of predicted values that are not used for correction. The experimental part of the study includes the numerical simulation of the three-body problem and a network of coupled oscillators with a fixed and variable integration step and finely confirms the theoretical findings.

Keywords: semi-explicit integration; predictor–corrector method; semi-explicit Adams–Bashforth–Moulton method; three-body problem; ODE solver (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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