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求解一维分数阶界面问题的自适应技术

Adaptive Technique for Solving 1-D Interface Problems of Fractional Order.

作者信息

Al-Masaeed Rahma, Maayah Banan, Abu-Ghurra Sana

机构信息

Department of Mathematics, Faculty of Science, The University of Jordan, Amman, 11942 Jordan.

Department of Mathematics, Faculty of Science, Ajloun National University, Ajloun, 26810 Jordan.

出版信息

Int J Appl Comput Math. 2022;8(4):214. doi: 10.1007/s40819-022-01397-z. Epub 2022 Aug 4.

DOI:10.1007/s40819-022-01397-z
PMID:35965734
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC9362368/
Abstract

In this paper, we present a numerical technique for solving 1-D interface problems of fractional order. This technique relies on the reproducing kernel functions and the shooting method. The biggest advantage over the existing standard analytical techniques is overcoming the difficulty arising in calculating complicated terms. Numerical examples are inspected to feature the significant highlights of this technique. Moreover, the solution procedure is simple, more effective and clearer.

摘要

在本文中，我们提出了一种求解一维分数阶界面问题的数值技术。该技术依赖于再生核函数和打靶法。相对于现有的标准解析技术，其最大优势在于克服了计算复杂项时出现的困难。通过数值算例考察了该技术的显著特点。此外，求解过程简单、更有效且更清晰。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/3663/9362368/7912570fd1a6/40819_2022_1397_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/3663/9362368/7c9c5d6a1d1e/40819_2022_1397_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/3663/9362368/75d82ca80d35/40819_2022_1397_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/3663/9362368/938e0695a509/40819_2022_1397_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/3663/9362368/b0685bd4650b/40819_2022_1397_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/3663/9362368/7912570fd1a6/40819_2022_1397_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/3663/9362368/7c9c5d6a1d1e/40819_2022_1397_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/3663/9362368/75d82ca80d35/40819_2022_1397_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/3663/9362368/938e0695a509/40819_2022_1397_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/3663/9362368/b0685bd4650b/40819_2022_1397_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/3663/9362368/7912570fd1a6/40819_2022_1397_Fig5_HTML.jpg

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本文引用的文献

1
Mathematical analysis of SIRD model of COVID-19 with Caputo fractional derivative based on real data.基于实际数据的具有卡普托分数阶导数的COVID-19 SIRD模型的数学分析
Results Phys. 2021 Feb;21:103772. doi: 10.1016/j.rinp.2020.103772. Epub 2020 Dec 29.
2
Modal analysis of circular Bragg fibers with arbitrary index profiles.具有任意折射率分布的圆形布拉格光纤的模态分析。
Opt Lett. 2006 Dec 1;31(23):3417-9. doi: 10.1364/ol.31.003417.