{"title":"变系数缓变时分数阶可动/不可动方程的快速Crank-Nicolson块中心差分格式","authors":"Yuexiu Dong, Lijuan Nong, An Chen","doi":"10.1002/mma.10701","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>In this paper, we are interest in developing efficient numerical scheme for solving a two-dimensional tempered time-fractional mobile/immobile equation with time-space dependent coefficients, which arises in the modeling of groundwater flow and pollutant transport. By applying the fast modified L1 formula in time and the block-centered difference method in space, we establish a fully discrete fast Crank-Nicolson difference scheme. The stability and error estimate of the proposed scheme are strictly proved. To handle the initial weakly singularity of the solution, we also consider a fast nonuniform modified L1 formula to solve the model problem. The numerical tests, both smooth and nonsmooth solution cases, are demonstrated to verify the accuracy and efficiency of our scheme.</p>\n </div>","PeriodicalId":49865,"journal":{"name":"Mathematical Methods in the Applied Sciences","volume":"48 6","pages":"6634-6646"},"PeriodicalIF":2.1000,"publicationDate":"2025-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fast Crank-Nicolson Block-Centered Difference Scheme for a Tempered Time-Fractional Mobile/Immobile Equation With Variable Coefficients\",\"authors\":\"Yuexiu Dong, Lijuan Nong, An Chen\",\"doi\":\"10.1002/mma.10701\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div>\\n \\n <p>In this paper, we are interest in developing efficient numerical scheme for solving a two-dimensional tempered time-fractional mobile/immobile equation with time-space dependent coefficients, which arises in the modeling of groundwater flow and pollutant transport. By applying the fast modified L1 formula in time and the block-centered difference method in space, we establish a fully discrete fast Crank-Nicolson difference scheme. The stability and error estimate of the proposed scheme are strictly proved. To handle the initial weakly singularity of the solution, we also consider a fast nonuniform modified L1 formula to solve the model problem. The numerical tests, both smooth and nonsmooth solution cases, are demonstrated to verify the accuracy and efficiency of our scheme.</p>\\n </div>\",\"PeriodicalId\":49865,\"journal\":{\"name\":\"Mathematical Methods in the Applied Sciences\",\"volume\":\"48 6\",\"pages\":\"6634-6646\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2025-01-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematical Methods in the Applied Sciences\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1002/mma.10701\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Methods in the Applied Sciences","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/mma.10701","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Fast Crank-Nicolson Block-Centered Difference Scheme for a Tempered Time-Fractional Mobile/Immobile Equation With Variable Coefficients
In this paper, we are interest in developing efficient numerical scheme for solving a two-dimensional tempered time-fractional mobile/immobile equation with time-space dependent coefficients, which arises in the modeling of groundwater flow and pollutant transport. By applying the fast modified L1 formula in time and the block-centered difference method in space, we establish a fully discrete fast Crank-Nicolson difference scheme. The stability and error estimate of the proposed scheme are strictly proved. To handle the initial weakly singularity of the solution, we also consider a fast nonuniform modified L1 formula to solve the model problem. The numerical tests, both smooth and nonsmooth solution cases, are demonstrated to verify the accuracy and efficiency of our scheme.
期刊介绍：
Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome.
Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted.
Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.
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