An improved Euler method for time fractional nonlinear subdiffusion equations with initial singularity
IF 1.7
3区 化学
Q3 CHEMISTRY, MULTIDISCIPLINARY
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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来源期刊
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.
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