Collocation-Based Approximation for a Time-Fractional Sub-Diffusion Model

IF 3.6 2区数学 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Fractal and Fractional Pub Date : 2023-08-31 DOI:10.3390/fractalfract7090657

Kaido Lätt, A. Pedas, Hanna Britt Soots, M. Vikerpuur

引用次数: 0

Abstract

We consider the numerical solution of a one-dimensional time-fractional diffusion problem, where the order of the Caputo time derivative belongs to (0, 1). Using the technique of the method of lines, we first develop from the original problem a system of fractional ordinary differential equations. Using an integral equation reformulation of this system, we study the regularity properties of the exact solution of the system of fractional differential equations and construct a piecewise polynomial collocation method to solve it numerically. We also investigate the convergence and the convergence order of the proposed method. To conclude, we present the results of some numerical experiments.

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基于配置的时间分数次扩散模型近似

考虑一类一维时间-分数阶扩散问题的数值解，其中Caputo时间导数阶为(0,1)。我们首先利用直线法的技巧，从原问题出发，建立了一个分数阶常微分方程组。利用分数阶微分方程组的积分方程重构，研究了分数阶微分方程组精确解的正则性，并构造了分段多项式配置法进行数值求解。研究了该方法的收敛性和收敛顺序。最后，我们给出了一些数值实验的结果。

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

Fractal and Fractional MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-

CiteScore

4.60

自引率

18.50%

发文量

632

审稿时长

11 weeks

期刊介绍： Fractal and Fractional is an international, scientific, peer-reviewed, open access journal that focuses on the study of fractals and fractional calculus, as well as their applications across various fields of science and engineering. It is published monthly online by MDPI and offers a cutting-edge platform for research papers, reviews, and short notes in this specialized area. The journal, identified by ISSN 2504-3110, encourages scientists to submit their experimental and theoretical findings in great detail, with no limits on the length of manuscripts to ensure reproducibility. A key objective is to facilitate the publication of detailed research, including experimental procedures and calculations. "Fractal and Fractional" also stands out for its unique offerings: it warmly welcomes manuscripts related to research proposals and innovative ideas, and allows for the deposition of electronic files containing detailed calculations and experimental protocols as supplementary material.