Effective Optimized Decomposition Algorithms for Solving Nonlinear Fractional Differential Equations

IF 1.9 4区 工程技术 Q3 ENGINEERING, MECHANICAL Journal of Computational and Nonlinear Dynamics Pub Date : 2022-11-23 DOI:10.1115/1.4056254
Marwa Laoubi, Z. Odibat, B. Maayah
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引用次数: 2

Abstract

In this paper, the optimized decomposition method, which was developed to solve integer-order differential equations, will be modified and extended to handle nonlinear fractional differential equations. Fractional derivatives will be considered in terms of Caputo sense. The suggested modifications design new optimized decompositions for the series solutions depending on linear approximations of the nonlinear equations. Two optimized decomposition algorithms have been introduced to obtain approximate solutions of broad classes of IVPs consisting of nonlinear fractional ODEs and PDEs. A comparative study was conducted between the proposed algorithms and the Adomian decomposition method by means of some test illustration problems. The implemented numerical simulation results showed that the proposed algorithms give better accuracy and convergence, and reduce the complexity of computational work compared to the Adomian's approach. This confirms the belief that the optimized decomposition method will be used effectively and widely as a powerful tool in solving various fractional differential equations.
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求解非线性分数阶微分方程的有效优化分解算法
在本文中,优化分解方法是为解决整阶微分方程而发展起来的,将其改进和推广到处理非线性分数阶微分方程。分数阶导数将根据卡普托意义来考虑。所建议的修改设计了基于非线性方程的线性近似的级数解的新的优化分解。介绍了两种优化分解算法,用于求解由非线性分数阶微分方程和偏微分方程组成的一类广义微分方程的近似解。通过若干试验实例问题,将所提算法与Adomian分解方法进行了比较研究。实现的数值模拟结果表明,与Adomian方法相比,本文提出的算法具有更好的精度和收敛性,并且减少了计算量。这证实了优化分解方法将作为求解各种分数阶微分方程的有力工具得到有效和广泛的应用。
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来源期刊
CiteScore
4.00
自引率
10.00%
发文量
72
审稿时长
6-12 weeks
期刊介绍: The purpose of the Journal of Computational and Nonlinear Dynamics is to provide a medium for rapid dissemination of original research results in theoretical as well as applied computational and nonlinear dynamics. The journal serves as a forum for the exchange of new ideas and applications in computational, rigid and flexible multi-body system dynamics and all aspects (analytical, numerical, and experimental) of dynamics associated with nonlinear systems. The broad scope of the journal encompasses all computational and nonlinear problems occurring in aeronautical, biological, electrical, mechanical, physical, and structural systems.
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