含变时滞泛函核分数阶积分方程的高精度半解析误差界分析方法

IF 1.6 4区 工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC
Ömür Kıvanç Kürkçü
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引用次数: 0

摘要

本文研究了具有泛函核和变时滞的分数阶积分方程,引入了一种基于stieltje - wigert多项式、矩阵展开式和拉普拉斯变换的高精度半解析方法。该方法将控制方程中的项解析转化为stieltje - wigert多项式型的矩阵展展开,将这些矩阵集合成一个唯一的矩阵方程,然后利用消元技术进行求解。并介绍了残差改进技术对得到的解进行修正。分别利用分数阶积分的代数性质和中值定理从理论上证明了残差界分析。用该方法处理了6个模型方程,并在设计的计算机程序上运行。根据结果,该方法可以直接处理模型方程并在数学软件上对其主机进行编码。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Hyperaccurate Semi–Analytical Method With Error Bound Analysis for Treating Fractional Integral Equations With Functional Kernels and Variable Delays

This study is concerned with treating the fractional integral equations with functional kernels and variable delays, introducing a hyperaccurate semi–analytical method based on the Stieltjes–Wigert polynomials, matrix expansions, and the Laplace transform. After analytically converting the terms in the governing equation into the matrix expansions of the Stieltjes–Wigert polynomials type at the collocation points, the method gathers these matrices into a unique matrix equation and then readily solves it by an elimination technique. The residual improvement technique is also introduced to correct the obtained solutions. The residual error bound analysis is theoretically proved via algebraical properties and the mean value theorem for fractional integral calculus, respectively. Six model equations are treated via the method, which runs on a devised computer program. Based on the outcomes, the method is straightforward to treat model equations and to encode its mainframe on a mathematical software.

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来源期刊
CiteScore
4.60
自引率
6.20%
发文量
101
审稿时长
>12 weeks
期刊介绍: Prediction through modelling forms the basis of engineering design. The computational power at the fingertips of the professional engineer is increasing enormously and techniques for computer simulation are changing rapidly. Engineers need models which relate to their design area and which are adaptable to new design concepts. They also need efficient and friendly ways of presenting, viewing and transmitting the data associated with their models. The International Journal of Numerical Modelling: Electronic Networks, Devices and Fields provides a communication vehicle for numerical modelling methods and data preparation methods associated with electrical and electronic circuits and fields. It concentrates on numerical modelling rather than abstract numerical mathematics. Contributions on numerical modelling will cover the entire subject of electrical and electronic engineering. They will range from electrical distribution networks to integrated circuits on VLSI design, and from static electric and magnetic fields through microwaves to optical design. They will also include the use of electrical networks as a modelling medium.
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