{"title":"A fourth-order compact ADI scheme for solving a two-dimensional time-fractional reaction-subdiffusion equation","authors":"Pradip Roul, Vikas Rohil","doi":"10.1007/s10910-024-01638-0","DOIUrl":null,"url":null,"abstract":"<div><p>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 <i>L</i>1 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 <span>\\({\\min {\\{2-\\alpha ,1+\\alpha \\}}}\\)</span> in the time direction, where <span>\\(\\alpha \\in (0,1)\\)</span> 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.</p></div>","PeriodicalId":648,"journal":{"name":"Journal of Mathematical Chemistry","volume":"62 8","pages":"2039 - 2055"},"PeriodicalIF":1.7000,"publicationDate":"2024-06-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Chemistry","FirstCategoryId":"92","ListUrlMain":"https://link.springer.com/article/10.1007/s10910-024-01638-0","RegionNum":3,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
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Abstract
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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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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