求解非线性分布阶分数阶Bagley-Torvik微分方程的谱配法

IF 3.6 2区 数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Ahmed Z. Amin, Mohamed A. Abdelkawy, Emad Solouma, Ibrahim Al-Dayel
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引用次数: 0

摘要

具有边界和初始条件的非线性分布阶分数阶Bagley-Torvik微分方程(DO-FBTE)是数值解分析中的一个问题。我们提出了一个基于移位勒让德高斯-洛巴托(SL-GL)配置技术的数值解来解决这个问题。将DO-FBTE的解近似为移位的勒让德多项式的截断序列,并将SL-GL配点作为插值节点。在SL-GL交点处计算残差。将DO-FBTE转化为可以用任何常规方法求解的代数方程组。通过一组数值算例验证了所提方案的准确性,并与已有结果进行了比较。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Spectral Collocation Method for Solving the Non-Linear Distributed-Order Fractional Bagley–Torvik Differential Equation
One of the issues in numerical solution analysis is the non-linear distributed-order fractional Bagley–Torvik differential equation (DO-FBTE) with boundary and initial conditions. We solve the problem by proposing a numerical solution based on the shifted Legendre Gauss–Lobatto (SL-GL) collocation technique. The solution of the DO-FBTE is approximated by a truncated series of shifted Legendre polynomials, and the SL-GL collocation points are employed as interpolation nodes. At the SL-GL quadrature points, the residuals are computed. The DO-FBTE is transformed into a system of algebraic equations that can be solved using any conventional method. A set of numerical examples is used to verify the proposed scheme’s accuracy and compare it to existing findings.
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来源期刊
Fractal and Fractional
Fractal and Fractional MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-
CiteScore
4.60
自引率
18.50%
发文量
632
审稿时长
11 weeks
期刊介绍: Fractal and Fractional is an international, scientific, peer-reviewed, open access journal that focuses on the study of fractals and fractional calculus, as well as their applications across various fields of science and engineering. It is published monthly online by MDPI and offers a cutting-edge platform for research papers, reviews, and short notes in this specialized area. The journal, identified by ISSN 2504-3110, encourages scientists to submit their experimental and theoretical findings in great detail, with no limits on the length of manuscripts to ensure reproducibility. A key objective is to facilitate the publication of detailed research, including experimental procedures and calculations. "Fractal and Fractional" also stands out for its unique offerings: it warmly welcomes manuscripts related to research proposals and innovative ideas, and allows for the deposition of electronic files containing detailed calculations and experimental protocols as supplementary material.
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