求解二维时间分数反应-次扩散方程的四阶紧凑 ADI 方案

IF 1.7 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Journal of Mathematical Chemistry Pub Date : 2024-06-25 DOI:10.1007/s10910-024-01638-0

Pradip Roul, Vikas Rohil

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引用次数: 0

摘要

本文旨在开发一种在两个空间维度上求解时间分数反应-次扩散（TFRSD）方程的计算方案。卡普托分数导数用于描述问题中出现的时间分数导数，并使用 L1 方案对其进行近似。空间导数的离散化采用了四阶紧凑差分方案。为了研究该方案的准确性，我们解决了一些测试问题。计算结果证实，该方案在空间方向上具有四阶收敛性，在时间方向上具有({\min {2-\alpha ,1+\alpha \)阶收敛性，其中$\alpha \in (0,1)$ 是分数导数的阶数。此外，还将计算结果与其他方法得出的结果进行了比较，以证明所提算法的优势。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

$A fourth-order compact ADI scheme for solving a two-dimensional time-fractional reaction-subdiffusion equation$

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A fourth-order compact ADI scheme for solving a two-dimensional time-fractional reaction-subdiffusion equation

This article aims at developing a computational scheme for solving the time fractional reaction-subdiffusion (TFRSD) equation in two space dimensions. The Caputo fractional derivative is used to describe the time-fractional derivative appearing in the problem and it is approximated by using the L1 scheme. A compact difference scheme of order four is utilized for discretization of the spatial derivatives. Some test problems are solved to investigate the accuracy of the scheme. The computed results confirm that the scheme has convergence of order four in space and an order of ${\min {\{2-\alpha ,1+\alpha \}}}$ in the time direction, where $\alpha \in (0,1)$ is the order of fractional derivative. Moreover, the computed results are compared with those obtained by other methods in order to justify the advantage of proposed algorithm.

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来源期刊

Journal of Mathematical Chemistry 化学-化学综合

CiteScore

3.70

自引率

17.60%

发文量

105

审稿时长

6 months

期刊介绍： The Journal of Mathematical Chemistry (JOMC) publishes original, chemically important mathematical results which use non-routine mathematical methodologies often unfamiliar to the usual audience of mainstream experimental and theoretical chemistry journals. Furthermore JOMC publishes papers on novel applications of more familiar mathematical techniques and analyses of chemical problems which indicate the need for new mathematical approaches. Mathematical chemistry is a truly interdisciplinary subject, a field of rapidly growing importance. As chemistry becomes more and more amenable to mathematically rigorous study, it is likely that chemistry will also become an alert and demanding consumer of new mathematical results. The level of complexity of chemical problems is often very high, and modeling molecular behaviour and chemical reactions does require new mathematical approaches. Chemistry is witnessing an important shift in emphasis: simplistic models are no longer satisfactory, and more detailed mathematical understanding of complex chemical properties and phenomena are required. From theoretical chemistry and quantum chemistry to applied fields such as molecular modeling, drug design, molecular engineering, and the development of supramolecular structures, mathematical chemistry is an important discipline providing both explanations and predictions. JOMC has an important role in advancing chemistry to an era of detailed understanding of molecules and reactions.