{"title":"新的稳定的、显式的、一阶的热传导方程求解方法","authors":"E. Kovács","doi":"10.32973/JCAM.2020.001","DOIUrl":null,"url":null,"abstract":"We introduce a novel explicit and stable numerical algorithm to solve the spatially discretized heat or diffusion equation. We compare the performance of the new method with analytical and numerical solutions. We show that the method is first order in time and can give approximate results for extremely large systems faster than the commonly used explicit or implicit methods.","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2019-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"13","resultStr":"{\"title\":\"New stable, explicit, first order method to solve the heat conduction equation\",\"authors\":\"E. Kovács\",\"doi\":\"10.32973/JCAM.2020.001\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We introduce a novel explicit and stable numerical algorithm to solve the spatially discretized heat or diffusion equation. We compare the performance of the new method with analytical and numerical solutions. We show that the method is first order in time and can give approximate results for extremely large systems faster than the commonly used explicit or implicit methods.\",\"PeriodicalId\":8424,\"journal\":{\"name\":\"arXiv: Computational Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2019-08-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"13\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: Computational Physics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.32973/JCAM.2020.001\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Computational Physics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.32973/JCAM.2020.001","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
New stable, explicit, first order method to solve the heat conduction equation
We introduce a novel explicit and stable numerical algorithm to solve the spatially discretized heat or diffusion equation. We compare the performance of the new method with analytical and numerical solutions. We show that the method is first order in time and can give approximate results for extremely large systems faster than the commonly used explicit or implicit methods.
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