{"title":"空间节制分数对流扩散模型的无条件稳定数值方法","authors":"Zeshan Qiu","doi":"10.1155/2024/6710903","DOIUrl":null,"url":null,"abstract":"A second-order numerical method for two-sided tempered fractional convection-diffusion equations is studied in this paper, both convection term and diffusion term are approximated by the tempered weighted and shifted Grünwald difference operators, the first time partial derivative is discretized by the Crank–Nicolson method, and then a class of second-order numerical schemes is derived. By means of matrix method, numerical schemes are proved to be unconditionally stable and convergent with order <span><svg height=\"13.8595pt\" style=\"vertical-align:-2.2681pt\" version=\"1.1\" viewbox=\"-0.0498162 -11.5914 35.65 13.8595\" width=\"35.65pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,9.387,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,13.885,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,20.167,-5.741)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,28.019,0)\"></path></g></svg><span></span><span><svg height=\"13.8595pt\" style=\"vertical-align:-2.2681pt\" version=\"1.1\" viewbox=\"38.506183799999995 -11.5914 16.394 13.8595\" width=\"16.394pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,38.556,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,45.264,-5.741)\"><use xlink:href=\"#g50-51\"></use></g><g transform=\"matrix(.013,0,0,-0.013,50.21,0)\"></path></g></svg>.</span></span> The validity of the proposed numerical scheme is verified by numerical experiments.","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"107 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"An Unconditionally Stable Numerical Method for Space Tempered Fractional Convection-Diffusion Models\",\"authors\":\"Zeshan Qiu\",\"doi\":\"10.1155/2024/6710903\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A second-order numerical method for two-sided tempered fractional convection-diffusion equations is studied in this paper, both convection term and diffusion term are approximated by the tempered weighted and shifted Grünwald difference operators, the first time partial derivative is discretized by the Crank–Nicolson method, and then a class of second-order numerical schemes is derived. 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An Unconditionally Stable Numerical Method for Space Tempered Fractional Convection-Diffusion Models
A second-order numerical method for two-sided tempered fractional convection-diffusion equations is studied in this paper, both convection term and diffusion term are approximated by the tempered weighted and shifted Grünwald difference operators, the first time partial derivative is discretized by the Crank–Nicolson method, and then a class of second-order numerical schemes is derived. By means of matrix method, numerical schemes are proved to be unconditionally stable and convergent with order . The validity of the proposed numerical scheme is verified by numerical experiments.
期刊介绍：
Journal of Mathematics is a broad scope journal that publishes original research articles as well as review articles on all aspects of both pure and applied mathematics. As well as original research, Journal of Mathematics also publishes focused review articles that assess the state of the art, and identify upcoming challenges and promising solutions for the community.
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