A Chebyshev collocation method for solving the non-linear variable-order fractional Bagley–Torvik differential equation

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-10-06 DOI:10.1515/ijnsns-2021-0395

A. Z. Amin, António M. Lopes, I. Hashim

引用次数: 3

Abstract

Abstract A numerical approach based on the shifted Chebyshev–Gauss collocation method is proposed for solving the non-linear variable-order fractional Bagley–Torvik differential equation (VO-FBTE), subject to initial and boundary conditions. The shifted fractional Chebyshev–Gauss collocation points are used as interpolation nodes, and the solution of the VO-FBTE is approximated by a truncated series of the shifted Chebyshev polynomials. The residuals are calculated at the shifted fractional Chebyshev–Gauss quadrature points. The original VO-FBTE is converted into a system of algebraic equations. The accuracy of the proposed scheme is confirmed with a set of numerical examples, and the results are compared with those obtained by other methods.

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求解非线性变阶分数阶Bagley-Torvik微分方程的Chebyshev配点法

摘要提出了一种基于移位Chebyshev–Gauss配置法的数值方法，用于求解非线性变阶分数阶Bagley–Torvik微分方程（VO-FBTE），并考虑初始和边界条件。移位的分数Chebyshev–Gauss配置点用作插值节点，VO-FBTE的解由移位的Chebyshef多项式的截断序列近似。残差是在移位的分数切比雪夫-高斯正交点上计算的。原始的VO-FBTE被转换成代数方程组。通过一组数值算例验证了该方案的准确性，并与其他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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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