时间分数阶四阶均匀Euler-Bernoulli钉钉梁方程的显式Chebyshev Petrov-Galerkin格式

IF 2.4 Q2 ENGINEERING, MECHANICAL
Mohamed Moustafa, Youssri Hassan Youssri, A. G. Atta
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引用次数: 3

摘要

本文建立了切比雪夫多项式的紧凑组合,并将其作为时间分数阶四阶欧拉-伯努利钉钉梁的空间基。该方法采用Petrov-Galerkin过程将微分问题离散为具有未知展开系数的线性代数方程组。利用有效的高斯消去法,我们求解了得到的具有特定模式矩阵的方程组。L∞{L_}{\infty和}l2 {l2}范{数估计误差界。通过三个算例验证了该算法的理论分析和有效性。}
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Explicit Chebyshev Petrov–Galerkin scheme for time-fractional fourth-order uniform Euler–Bernoulli pinned–pinned beam equation
Abstract In this research, a compact combination of Chebyshev polynomials is created and used as a spatial basis for the time fractional fourth-order Euler–Bernoulli pinned–pinned beam. The method is based on applying the Petrov–Galerkin procedure to discretize the differential problem into a system of linear algebraic equations with unknown expansion coefficients. Using the efficient Gaussian elimination procedure, we solve the obtained system of equations with matrices of a particular pattern. The L ∞ {L}_{\infty } and L 2 {L}_{2} norms estimate the error bound. Three numerical examples were exhibited to verify the theoretical analysis and efficiency of the newly developed algorithm.
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来源期刊
CiteScore
6.20
自引率
3.60%
发文量
49
审稿时长
44 weeks
期刊介绍: The Journal of Nonlinear Engineering aims to be a platform for sharing original research results in theoretical, experimental, practical, and applied nonlinear phenomena within engineering. It serves as a forum to exchange ideas and applications of nonlinear problems across various engineering disciplines. Articles are considered for publication if they explore nonlinearities in engineering systems, offering realistic mathematical modeling, utilizing nonlinearity for new designs, stabilizing systems, understanding system behavior through nonlinearity, optimizing systems based on nonlinear interactions, and developing algorithms to harness and leverage nonlinear elements.
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