An Adaptive Difference Method for Variable-Order Diffusion Equations

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-06-25 DOI:10.1007/s00009-024-02681-6

Joaquín Quintana-Murillo, Santos Bravo Yuste

引用次数: 0

Abstract

An adaptive finite difference scheme for variable-order fractional-time subdiffusion equations in the Caputo form is studied. The fractional-time derivative is discretized by the L1 procedure but using nonhomogeneous timesteps. The size of these timesteps is chosen by an adaptive algorithm to keep the local error bounded around a preset value, a value that can be chosen at will. For some types of problems, this adaptive method is much faster than the corresponding usual method with fixed timesteps while keeping the local error of the numerical solution around the preset values. These findings turn out to be similar to those found for constant-order fractional diffusion equations.

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变阶扩散方程的自适应差分法

研究了卡普托形式的变阶分数-时间亚扩散方程的自适应有限差分方案。分时导数采用 L1 程序离散化，但使用非均质时间步长。这些时间步的大小由自适应算法选择，以保持局部误差在预设值附近有界，这个值可以随意选择。对于某些类型的问题，这种自适应方法比采用固定时间步长的相应普通方法要快得多，同时还能将数值解的局部误差保持在预设值附近。这些发现与恒阶分数扩散方程的发现相似。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.