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

IF 1.1 4区工程技术 Q4 THERMODYNAMICS

Thermal Science Pub Date : 2023-01-01 DOI:10.2298/tsci23s1195s

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

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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.

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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。

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来源期刊

Thermal Science 工程技术-热力学

CiteScore

2.70

自引率

29.40%

发文量

399

审稿时长

5 months

期刊介绍： The main aims of Thermal Science to publish papers giving results of the fundamental and applied research in different, but closely connected fields: fluid mechanics (mainly turbulent flows), heat transfer, mass transfer, combustion and chemical processes in single, and specifically in multi-phase and multi-component flows in high-temperature chemically reacting flows processes present in thermal engineering, energy generating or consuming equipment, process and chemical engineering equipment and devices, ecological engineering, The important characteristic of the journal is the orientation to the fundamental results of the investigations of different physical and chemical processes, always jointly present in real conditions, and their mutual influence. To publish papers written by experts from different fields: mechanical engineering, chemical engineering, fluid dynamics, thermodynamics and related fields. To inform international scientific community about the recent, and most prominent fundamental results achieved in the South-East European region, and particularly in Serbia, and - vice versa - to inform the scientific community from South-East European Region about recent fundamental and applied scientific achievements in developed countries, serving as a basis for technology development. To achieve international standards of the published papers, by the engagement of experts from different countries in the International Advisory board.