求解粘弹性柱模型中一类分数阶偏微分方程的Laguerre小波谱法

IF 5.3 1区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Chaos Solitons & Fractals Pub Date : 2025-01-18 DOI:10.1016/j.chaos.2025.116010

Z. Mahmoudi , M. Mehdizadeh Khalsaraei , M. Nosrati Sahlan , A. Shokri

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引用次数: 0

摘要

各种材料的力学性能都会受到外力的影响。本文的目的是研究卡普托意义下粘弹性柱动力的分数阶。为此，构造了拉盖尔小波及其整数阶和分数阶运算矩阵，并利用它们将主要的分数阶问题简化为若干代数方程。然后，将得到的方程在确定的配置节点中离散化。从而得到一个代数系统，通过求解得到主要问题的近似解。为了说明该方法的准确性和有效性，给出了一些算例，并将数值结果与其他几种方法的结果进行了比较。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Laguerre wavelets spectral method for solving a class of fractional order PDEs arising in viscoelastic column modeling

The mechanical properties of the various materials could be influenced by external forces. The aim of this paper is to study the fractional order of viscoelastic column dynamic in Caputo sense. For this purpose, Laguerre wavelets and their operational matrices of integer and fractional orders are constructed and utilized to reduce the main fractional problem to some algebraic equation. Then, the obtained equation is discretized in the determined collocation nodes. Therefore an algebraic system is achieved that by solving it, the approximated solution of main problem is obtained. For showing the accuracy and efficiency of the purposed method, some illustrative examples are provided and the numerical results are compared with the results of some other approaches.

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来源期刊

Chaos Solitons & Fractals 物理-数学跨学科应用

CiteScore

13.20

自引率

10.30%

发文量

1087

审稿时长

9 months

期刊介绍： Chaos, Solitons & Fractals strives to establish itself as a premier journal in the interdisciplinary realm of Nonlinear Science, Non-equilibrium, and Complex Phenomena. It welcomes submissions covering a broad spectrum of topics within this field, including dynamics, non-equilibrium processes in physics, chemistry, and geophysics, complex matter and networks, mathematical models, computational biology, applications to quantum and mesoscopic phenomena, fluctuations and random processes, self-organization, and social phenomena.