{"title":"A Reduced-Order Finite Difference Scheme Based on POD for Fractional Stochastic Advection–Diffusion Equation","authors":"Z. Soori, A. Aminataei, D. Baleanu","doi":"10.1007/s40995-023-01490-y","DOIUrl":null,"url":null,"abstract":"<div><p>This article introduces a new scheme for the fractional stochastic advection–diffusion equation (FSA-DE) in time where the fractional term is expressed in Caputo sence of order <span>\\(\\alpha \\)</span> <span>\\((0<\\alpha <1)\\)</span>. First, an L1 approximation is employed to estimate the Caputo derivative. Then, the spatial derivative is approximated by a second-order finite difference scheme. Moreover, we combine the implicit finite difference (IFD) scheme with the proper orthogonal decomposition (POD) method to reduce the used CPU time. In other words, the POD based reduced-order IFD scheme is obtained. The proposed scheme can be regarded as the modification of the exiting work (Mirzaee et al. in J Sci Technol Trans Sci 45:607–617, 2001). The numerical results are provided to confirm the feasibility and efficiency of the proposed method.</p></div>","PeriodicalId":600,"journal":{"name":"Iranian Journal of Science and Technology, Transactions A: Science","volume":"47 4","pages":"1299 - 1311"},"PeriodicalIF":1.4000,"publicationDate":"2023-07-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40995-023-01490-y.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Iranian Journal of Science and Technology, Transactions A: Science","FirstCategoryId":"4","ListUrlMain":"https://link.springer.com/article/10.1007/s40995-023-01490-y","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
引用次数: 0
Abstract
This article introduces a new scheme for the fractional stochastic advection–diffusion equation (FSA-DE) in time where the fractional term is expressed in Caputo sence of order \(\alpha \)\((0<\alpha <1)\). First, an L1 approximation is employed to estimate the Caputo derivative. Then, the spatial derivative is approximated by a second-order finite difference scheme. Moreover, we combine the implicit finite difference (IFD) scheme with the proper orthogonal decomposition (POD) method to reduce the used CPU time. In other words, the POD based reduced-order IFD scheme is obtained. The proposed scheme can be regarded as the modification of the exiting work (Mirzaee et al. in J Sci Technol Trans Sci 45:607–617, 2001). The numerical results are provided to confirm the feasibility and efficiency of the proposed method.
本文介绍了分数阶随机平流扩散方程(FSA-DE)的一种新格式，其中分数阶项用Caputo阶序表示\(\alpha \)\((0<\alpha <1)\)。首先，采用L1近似估计卡普托导数。然后，用二阶有限差分格式逼近空间导数。此外，我们将隐式有限差分(IFD)格式与适当的正交分解(POD)方法相结合，以减少所使用的CPU时间。也就是说，得到了基于POD的降阶IFD格式。所提出的方案可以看作是对现有工作的修改(Mirzaee et al. in J Sci technology l Trans Sci 45:607-617, 2001)。数值结果验证了该方法的可行性和有效性。
期刊介绍：
The aim of this journal is to foster the growth of scientific research among Iranian scientists and to provide a medium which brings the fruits of their research to the attention of the world’s scientific community. The journal publishes original research findings – which may be theoretical, experimental or both - reviews, techniques, and comments spanning all subjects in the field of basic sciences, including Physics, Chemistry, Mathematics, Statistics, Biology and Earth Sciences
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