基于Gegenbauer小波的广义时空分数阶Klein-Gordon方程数值模拟

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-10-14 DOI:10.1515/ijnsns-2021-0304

M. Faheem, Arshad Khan, Muslim Malik, A. Debbouche

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引用次数: 0

摘要

摘要本文利用Gegenbauer小波方法研究了广义时空分数阶Klein–Gordon方程的数值解。所开发的方法利用了Gegenbauer小波的分数阶积分算子（FOIO），该算子是利用Riemann-Liouville分数阶积分（RLFI）算子的定义和拉普拉斯变换构造的。该算法基于Gegenbauer小波与FOIO相结合，将GSTFKGE转化为利用牛顿技术求解的方程组。此外，还计算了所提出方法的误差范数上限，以验证所提出方法在理论上的真实性。数值结果与文献和图解中现有结果的比较表明了我们方法的准确性和可靠性。

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Numerical simulation for generalized space-time fractional Klein–Gordon equations via Gegenbauer wavelet

Abstract This paper investigates numerical solution of generalized space-time fractional Klein–Gordon equations (GSTFKGE) by using Gegenbauer wavelet method (GWM). The developed method makes use of fractional order integral operator (FOIO) for Gegenbauer wavelet, which is constructed by employing the definition of Riemann–Liouville fractional integral (RLFI) operator and Laplace transformation. The present algorithm is based on Gegenbauer wavelet jointly with FOIO to convert a GSTFKGE into a system of equations which is solved by using Newton’s technique. Additionally, the upper bound of error norm of the proposed method is calculated to validate the theoretical authenticity of the developed method. The comparison of numerical outcomes with the existing results in the literature and graphical illustrations show the accuracy and reliability of our method.

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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.