Guedes, Priscila F.S. and Mendes, Eduardo M.A.M. and Nepomuceno, Erivelton (2022) Effective computational discretization scheme for nonlinear dynamical systems. Applied Mathematics and Computation, 428 (127207). pp. 1-15. ISSN 0096-3003

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Abstract

Numerical methods are essential to investigate and apply nonlinear continuous-time dynamical systems in many fields of science and engineering and discretization schemes are required to obtain the solutions of such dynamical systems. Although computing power has been speedily growing in recent decades, embedded and large-scale problems have motivated significant research to improve the computational efficiency. Nevertheless, few studies have focused on finite precision limitation on discretization schemes due to round-off effects in floating-point number representation. In this paper, a computational effective discretization scheme for nonlinear dynamical systems is introduced. By means of a theorem, it is shown that high-order terms in the Runge-Kutta method can be neglected with no accuracy loss. The proposed approach is illustrated using three well-known systems, namely the Rössler systems, the Lorenz equations and the Sprott B system. The number of mathematical operations and simulation time have reduced up to 81.1% and 90.7%, respectively. Furthermore, as the step-size decreases, the number of neglected terms increases due to the precision of the computer. Yet, accuracy, observability of dynamical systems and the largest Lyapunov are preserved. The adapted scheme is effective, reliable and suitable for embedded and large-scale applications.

Item Type:	Article
Keywords:	chaos; Nonlinear dynamics; Computer simulation; Computer arithmetic; Observability; Green algorithms;
Academic Unit:	Faculty of Science and Engineering > Electronic Engineering Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	18268
Identification Number:	https://doi.org/10.1016/j.amc.2022.127207
Depositing User:	Erivelton Nepomuceno
Date Deposited:	12 Mar 2024 16:20
Journal or Publication Title:	Applied Mathematics and Computation
Publisher:	Elsevier
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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