NUMERICAL ANALYSIS OF THE DUFFING EQUATION: A COMPARATIVE STUDY

Q2 Multidisciplinary

Xinan Jiaotong Daxue Xuebao/Journal of Southwest Jiaotong University Pub Date : 2023-01-01 DOI:10.35741/issn.0258-2724.58.4.94

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Abstract

This research aims to carry out an exhaustive comparison between the formulation of the finite difference method and the Runge-Kutta method as numerical approaches to determine the solution of the Duffing oscillator. The Duffing oscillator represented by a nonlinear second-order differential equation, exhibits complex and fascinating dynamics that include bifurcations and periodic orbits in specific regions of its parameters. The purpose of this article is to analyze in detail the results obtained by both methods, highlighting the advantages and limitations of each one in terms of precision, stability, and computational efficiency. The findings of this study offer a deeper perspective on the suitability of the finite difference and Runge-Kutta methods for the numerical resolution of problems involving the Duffing oscillator and contribute to the development of more effective numerical tools for the analysis of nonlinear dynamic systems. Keywords: Discretization, Finite Differences, Convergence, The Runge-Kutta Method, The Duffing Equation DOI： https://doi.org/10.35741/issn.0258-2724.58.4.94

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duffing方程的数值分析:比较研究

本研究旨在对有限差分法和龙格-库塔法作为确定Duffing振子解的数值方法进行详尽的比较。由非线性二阶微分方程表示的Duffing振子表现出复杂而迷人的动力学，包括在其参数的特定区域的分岔和周期轨道。本文的目的是详细分析两种方法得到的结果，突出每种方法在精度、稳定性和计算效率方面的优点和局限性。本研究的发现为有限差分和龙格-库塔方法在Duffing振荡器数值求解问题中的适用性提供了更深入的视角，并有助于开发更有效的非线性动力系统分析数值工具。关键词:离散化，有限差分，收敛，龙格-库塔方法，Duffing方程DOI: https://doi.org/10.35741/issn.0258-2724.58.4.94

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来源期刊

Xinan Jiaotong Daxue Xuebao/Journal of Southwest Jiaotong University Multidisciplinary-Multidisciplinary

CiteScore

1.50

自引率

0.00%

发文量

166

期刊介绍： Information not localized