Stability and numerical solutions for second-order ordinary differential equations with application in mechanical systems

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Title: Stability and numerical solutions for second-order ordinary differential equations with application in mechanical systems
Authors: Turab, Ali | Montoyo, Andres | Nescolarde-Selva, Josué Antonio
Research Group/s: Procesamiento del Lenguaje y Sistemas de Información (GPLSI) | Sistémica y Cibernética (SYC)
Center, Department or Service: Universidad de Alicante. Departamento de Lenguajes y Sistemas Informáticos | Universidad de Alicante. Departamento de Matemática Aplicada
Keywords: Differential equations | Solutions | Numerical computations | Stability analysis | Applications
Issue Date: 4-Jul-2024
Publisher: Springer Nature
Citation: Journal of Applied Mathematics and Computing. 2024, 70: 5103-5128. https://doi.org/10.1007/s12190-024-02175-4
Abstract: This study undertakes a comprehensive analysis of second-order Ordinary Differential Equations (ODEs) to examine animal avoidance behaviors, specifically emphasizing analytical and computational aspects. By using the Picard–Lindelöf and fixed-point theorems, we prove the existence of unique solutions and examine their stability according to the Ulam-Hyers criterion. We also investigate the effect of external forces and the system’s sensitivity to initial conditions. This investigation applies Euler and Runge–Kutta fourth-order (RK4) methods to a mass-spring-damper system for numerical approximation. A detailed analysis of the numerical approaches, including a rigorous evaluation of both absolute and relative errors, demonstrates the efficacy of these techniques compared to the exact solutions. This robust examination enhances the theoretical foundations and practical use of such ODEs in understanding complex behavioral patterns, showcasing the connection between theoretical understanding and real-world applications.
Sponsor: Open Access funding provided thanks to the CRUE-CSIC agreement with Springer Nature. This research is supported by the University of Alicante, Spain, the Spanish Ministry of Science and Innovation, the Generalitat Valenciana, Spain, and the European Regional Development Fund (ERDF) through the following funding: At the national level, the following projects were granted: TRIVIAL (PID2021-122263OB-C22); and CORTEX (PID2021-123956OB-I00), funded by MCIN/AEI/10.13039/501100011033 and, as appropriate, by “ERDF A way of making Europe”, by the“European Union” or by the “European Union NextGenerationEU/PRTR”. At regional level, the Generalitat Valenciana (Conselleria d’Educacio, Investigacio, Cultura i Esport), Spain, granted funding for NL4DISMIS (CIPROM/2021/21).
URI: http://hdl.handle.net/10045/144906
ISSN: 1598-5865 (Print) | 1865-2085 (Online)
DOI: 10.1007/s12190-024-02175-4
Language: eng
Type: info:eu-repo/semantics/article
Rights: © The Author(s) 2024. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Peer Review: si
Publisher version: https://doi.org/10.1007/s12190-024-02175-4
Appears in Collections:INV - SYC - Artículos de Revistas
INV - GPLSI - Artículos de Revistas

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