An improved Euler method for time fractional nonlinear subdiffusion equations with initial singularity

IF 1.7 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Journal of Mathematical Chemistry Pub Date : 2024-11-16 DOI:10.1007/s10910-024-01693-7

Junlan Lv, Jianfei Huang, Sadia Arshad

引用次数: 0

Abstract

As is known that many existing numerical methods for time fractional nonlinear subdiffusion equations (TFNSEs) often suffer from the phenomenon of order reduction, because the solution of TFNSEs usually has the initial singularity. To overcome this order reduction problem, in this paper, an improved Euler method is proposed for solving TFNSEs based on the technique of variable transformation in time. Then, it is proved that the temporal convergence order of the proposed method is the first order for any fractional order \(\alpha \in (0,1)\), which achieves the optimal convergence order of the Euler method. Finally, numerical experiments are given to verify the correctness of our theoretical results.

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具有初始奇异性的时间分数阶非线性次扩散方程的改进欧拉方法

众所周知，由于时间分数阶非线性亚扩散方程的解通常具有初始奇异性，现有的许多求解时间分数阶非线性亚扩散方程的数值方法往往存在降阶现象。为了克服这一降阶问题，本文提出了一种基于时间变量变换技术的改进欧拉法求解tfnse。然后，证明了所提方法的时间收敛阶对任意分数阶\(\alpha \in (0,1)\)均为一阶，达到了欧拉方法的最优收敛阶。最后通过数值实验验证了理论结果的正确性。

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

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.