Numerical simulation of variable-order fractional differential equation of nonlinear Lane–Emden type appearing in astrophysics

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-04-28 DOI:10.1515/ijnsns-2021-0092

Rupali Gupta, S. Kumar

引用次数: 2

Abstract

Abstract This paper suggests the Chebyshev pseudo-spectral approach to solve the variable-order fractional Lane–Emden differential equations (VOFLEDE). The variable-order fractional derivative (VOFD) is defined in the Caputo sense. The proposed method transforms the problem into a set of algebraic equations that can be solved for unknowns. Few examples are discussed to exhibit the viability and effectiveness of the approach. The present study indicates the accuracy, efficiency, and powerfulness of the Chebyshev collocation method in solving the VOFD Lane–Emden equation. Error bound and convergence analysis of the method is also discussed. It is worth noticing that using lesser collocation nodes in computation is another advantage of the technique, which eventually reduces the computational cost.

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天体物理学中非线性Lane-Emden型变阶分数阶微分方程的数值模拟

提出了求解变阶分数阶Lane-Emden微分方程的Chebyshev伪谱方法。变阶分数阶导数(VOFD)是在卡普托意义下定义的。该方法将该问题转化为一组可以求解未知数的代数方程。文中还讨论了几个例子来说明该方法的可行性和有效性。本研究表明，切比雪夫配点法在求解VOFD Lane-Emden方程中的准确性、效率和功能。讨论了该方法的误差界和收敛性分析。值得注意的是，在计算中使用较少的并置节点是该技术的另一个优点，它最终降低了计算成本。

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

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.