An efficient matrix method for coupled systems of variable fractional order differential equations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2023-01-01 DOI:10.2298/tsci23s1195s

K. Shah, Bahaaeldin Abdalla, T. Abdeljawad, I. Suwan

{"title":"An efficient matrix method for coupled systems of variable fractional order differential equations","authors":"K. Shah, Bahaaeldin Abdalla, T. Abdeljawad, I. Suwan","doi":"10.2298/tsci23s1195s","DOIUrl":null,"url":null,"abstract":"We establish a powerful numerical algorithm to compute numerical solutions of coupled system of variable fractional order differential equations. Our numer?ical procedure is based on Bernstein polynomials. The mentioned polynomials are non-orthogonal and have the ability to produce good numerical results as compared to some other numerical method like wavelet. By variable fractional order differentiation and integration, some operational matrices are formed. On using the obtained matrices, the proposed coupled system is reduced to a system of algebraic equations. Using MATLAB, we solve the given equation for required results. Graphical presentations and maximum absolute errors are given to illustrate the results. Some useful features of our sachem are those that we need no discretization or collocation technique prior to develop operational matrices. Due to these features the computational complexity is much more reduced. Further, the efficacy of the procedure is enhanced by increasing the scale level. We also compare our results with that of Haar wavelet method to justify the useful?ness of our adopted method.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.2298/tsci23s1195s","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 1

Abstract

We establish a powerful numerical algorithm to compute numerical solutions of coupled system of variable fractional order differential equations. Our numer?ical procedure is based on Bernstein polynomials. The mentioned polynomials are non-orthogonal and have the ability to produce good numerical results as compared to some other numerical method like wavelet. By variable fractional order differentiation and integration, some operational matrices are formed. On using the obtained matrices, the proposed coupled system is reduced to a system of algebraic equations. Using MATLAB, we solve the given equation for required results. Graphical presentations and maximum absolute errors are given to illustrate the results. Some useful features of our sachem are those that we need no discretization or collocation technique prior to develop operational matrices. Due to these features the computational complexity is much more reduced. Further, the efficacy of the procedure is enhanced by increasing the scale level. We also compare our results with that of Haar wavelet method to justify the useful?ness of our adopted method.

查看原文本刊更多论文

变分数阶微分方程耦合系统的有效矩阵法

建立了一种计算变分数阶微分方程耦合系统数值解的强大数值算法。我们的号码吗?逻辑程序是基于伯恩斯坦多项式的。上述多项式是非正交的，与小波等其他数值方法相比，具有产生良好数值结果的能力。通过变分数阶微分和积分，得到了一些可操作矩阵。利用得到的矩阵，将所提出的耦合系统简化为一个代数方程组。利用MATLAB对给定方程进行求解，得到所需结果。给出了图形表示和最大绝对误差来说明结果。我们的sachem的一些有用的特征是，在开发运算矩阵之前，我们不需要离散化或搭配技术。由于这些特征，计算复杂度大大降低。此外，通过增加规模水平，提高了程序的有效性。我们还将我们的结果与Haar小波方法的结果进行了比较，以证明该方法的实用性。我们所采用的方法。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.