{"title":"求解二维分数阶扩散方程的一种新的数值格式","authors":"Dilara Altan Koç, Mustafa Gülsu","doi":"10.17512/jamcm.2021.2.01","DOIUrl":null,"url":null,"abstract":"In this study, the locally one dimensional (LOD) method is used to solve the two dimensional time fractional diffusion equation. The fractional derivative is the Caputo fractional derivative of order α. The rate of convergence of the finite difference method is presented. It is seen that this method is in agreement with the obtained numerical solutions with acceptable central processing unit time (CPU time). Error estimates, numerical and exact results are tabulated. The graphics of errors are given. MSC 2010: 65M06, 65M22, 34K37","PeriodicalId":43867,"journal":{"name":"Journal of Applied Mathematics and Computational Mechanics","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A new numerical scheme for solving the two dimensional fractional diffusion equation\",\"authors\":\"Dilara Altan Koç, Mustafa Gülsu\",\"doi\":\"10.17512/jamcm.2021.2.01\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this study, the locally one dimensional (LOD) method is used to solve the two dimensional time fractional diffusion equation. The fractional derivative is the Caputo fractional derivative of order α. The rate of convergence of the finite difference method is presented. It is seen that this method is in agreement with the obtained numerical solutions with acceptable central processing unit time (CPU time). Error estimates, numerical and exact results are tabulated. The graphics of errors are given. MSC 2010: 65M06, 65M22, 34K37\",\"PeriodicalId\":43867,\"journal\":{\"name\":\"Journal of Applied Mathematics and Computational Mechanics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2021-06-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied Mathematics and Computational Mechanics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.17512/jamcm.2021.2.01\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied Mathematics and Computational Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.17512/jamcm.2021.2.01","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
A new numerical scheme for solving the two dimensional fractional diffusion equation
In this study, the locally one dimensional (LOD) method is used to solve the two dimensional time fractional diffusion equation. The fractional derivative is the Caputo fractional derivative of order α. The rate of convergence of the finite difference method is presented. It is seen that this method is in agreement with the obtained numerical solutions with acceptable central processing unit time (CPU time). Error estimates, numerical and exact results are tabulated. The graphics of errors are given. MSC 2010: 65M06, 65M22, 34K37
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