解决时空分数阶波方程的保角映射和切比雪夫配位法混合技术

IF 1.6 4区 工程技术 Q3 ENGINEERING, ELECTRICAL & ELECTRONIC
Adel Abd Elaziz El-Sayed, Salah Boulaaras
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引用次数: 0

摘要

这项研究提出了一种求解时空分数阶波方程的数值方法。时间分数导数是在保角意义上描述的,而空间分数导数是在卡普托意义上给出的。所研究的技术基于第三类移位切比雪夫多项式。利用保角映射、卡普托导数和第三类移位切比雪夫多项式的特性,将主要问题转换为常微分方程组。然后,利用切比雪夫配位法和非标准有限差分法将该系统转换为代数方程系统。最后,可以通过牛顿迭代法对该系统进行数值求解。最后,将提供物理数值示例和比较结果,以证实所建议方法的准确性、适用性和高效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Hybrid technique of conformal mapping and Chebyshev collocation method for solving time–space fractional order wave equation

This work presents a numerical approach for solving the time–space fractional-order wave equation. The time-fractional derivative is described in the conformal sense, whereas the space-fractional derivative is given in the Caputo sense. The investigated technique is based on the third-kind of shifted Chebyshev polynomials. The main problem is converted into a system of ordinary differential equations using conformal mapping, Caputo derivatives, and the properties of the third-kind shifted Chebyshev polynomials. Then, the Chebyshev collocation method and the non-standard finite difference method will be used to convert this system into a system of algebraic equations. Finally, this system can be solved numerically via Newton's iteration method. In the end, physics numerical examples and comparison results are provided to confirm the accuracy, applicability, and efficiency of the suggested approach.

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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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