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

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

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引用次数: 3

摘要

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。

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

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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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

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.