{"title":"求解次扩散方程的广义Crank-Nicolson方法","authors":"M. Błasik","doi":"10.1109/MMAR.2018.8485908","DOIUrl":null,"url":null,"abstract":"In this paper we present a numerical solution of a one-dimensional subdiffusion equation with a fractional time derivative in the Caputo sense. The proposed algorithm is an extension of the Crank-Nicolson method for a classical parabolic partial differential equation. In the final part, we also present examples illustrating the comparison of the analytical solution with the results received by the proposed numerical method.","PeriodicalId":201658,"journal":{"name":"2018 23rd International Conference on Methods & Models in Automation & Robotics (MMAR)","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2018-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"A Generalized Crank-Nicolson Method for the Solution of the Subdiffusion Equation\",\"authors\":\"M. Błasik\",\"doi\":\"10.1109/MMAR.2018.8485908\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper we present a numerical solution of a one-dimensional subdiffusion equation with a fractional time derivative in the Caputo sense. The proposed algorithm is an extension of the Crank-Nicolson method for a classical parabolic partial differential equation. In the final part, we also present examples illustrating the comparison of the analytical solution with the results received by the proposed numerical method.\",\"PeriodicalId\":201658,\"journal\":{\"name\":\"2018 23rd International Conference on Methods & Models in Automation & Robotics (MMAR)\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2018 23rd International Conference on Methods & Models in Automation & Robotics (MMAR)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/MMAR.2018.8485908\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2018 23rd International Conference on Methods & Models in Automation & Robotics (MMAR)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/MMAR.2018.8485908","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A Generalized Crank-Nicolson Method for the Solution of the Subdiffusion Equation
In this paper we present a numerical solution of a one-dimensional subdiffusion equation with a fractional time derivative in the Caputo sense. The proposed algorithm is an extension of the Crank-Nicolson method for a classical parabolic partial differential equation. In the final part, we also present examples illustrating the comparison of the analytical solution with the results received by the proposed numerical method.
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