An Unconditionally Stable Numerical Method for Space Tempered Fractional Convection-Diffusion Models

IF 1.3 4区数学 Q1 MATHEMATICS Journal of Mathematics Pub Date : 2024-05-31 DOI:10.1155/2024/6710903

Zeshan Qiu

{"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. 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":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1155/2024/6710903","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

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 . The validity of the proposed numerical scheme is verified by numerical experiments.

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

空间节制分数对流扩散模型的无条件稳定数值方法

本文研究了双面节制分式对流扩散方程的二阶数值方法，对流项和扩散项都用节制加权和移位格吕内瓦尔德差分算子近似，第一次偏导数用 Crank-Nicolson 方法离散，然后推导出一类二阶数值方案。通过矩阵法证明了数值方案的无条件稳定性和阶收敛性。通过数值实验验证了所提出数值方案的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文去求助

来源期刊

Journal of Mathematics Mathematics-General Mathematics

CiteScore

2.50

自引率

14.30%

发文量

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.