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基于一致型 Caputo 非多项式样条方法对分数阶 Korteweg-de Vries 方程的高效模拟。

Efficient simulation of Time-Fractional Korteweg-de Vries equation via conformable-Caputo non-Polynomial spline method.

机构信息

Department of Mathematics, College of Education, University of Zakho, Duhok, Iraq.

Department of Mathematics, College of Education, University of Sulaimani, Sulaimani, Iraq.

出版信息

PLoS One. 2024 Jun 26;19(6):e0303760. doi: 10.1371/journal.pone.0303760. eCollection 2024.

DOI:10.1371/journal.pone.0303760
PMID:38923964
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC11207126/
Abstract

This research presents a novel conformable-Caputo fractional non-polynomial spline method for solving the time-fractional Korteweg-de Vries (KdV) equation. Emphasizing numerical analysis and algorithm development, the method offers enhanced precision and modeling capabilities. Evaluation via the Von Neumann method demonstrates unconditional stability within defined parameters. Comparative analysis, supported by contour and 2D/3D graphs, validates the method's accuracy and efficiency against existing approaches. Quantitative assessment using L2 and L∞ error norms confirms its superiority. In conclusion, the study proposes a robust solution for the time-fractional KdV equation.

摘要

本研究提出了一种新颖的一致 Caputo 分数非多项式样条方法，用于求解时间分数 Korteweg-de Vries（KdV）方程。该方法强调数值分析和算法开发，提供了更高的精度和建模能力。通过冯·诺依曼方法评估，在定义的参数范围内证明了无条件稳定性。通过轮廓图和 2D/3D 图进行的比较分析，验证了该方法相对于现有方法的准确性和效率。使用 L2 和 L∞误差范数的定量评估证实了其优越性。总之，本研究提出了一种用于时间分数 KdV 方程的鲁棒解决方案。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7052/11207126/75ed97e409cc/pone.0303760.g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7052/11207126/11577af35598/pone.0303760.g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7052/11207126/2a25b84c5455/pone.0303760.g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7052/11207126/c50a1e8f6e6e/pone.0303760.g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7052/11207126/7206f91adf82/pone.0303760.g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7052/11207126/7ee647bbfeea/pone.0303760.g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7052/11207126/2118183311fb/pone.0303760.g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7052/11207126/75ed97e409cc/pone.0303760.g007.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7052/11207126/11577af35598/pone.0303760.g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7052/11207126/2a25b84c5455/pone.0303760.g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7052/11207126/c50a1e8f6e6e/pone.0303760.g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7052/11207126/7206f91adf82/pone.0303760.g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7052/11207126/7ee647bbfeea/pone.0303760.g005.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7052/11207126/2118183311fb/pone.0303760.g006.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7052/11207126/75ed97e409cc/pone.0303760.g007.jpg

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