{"title":"拉普拉斯方程有限差分解析解与数值解的误差估计","authors":"Alcyone César Pereira Silva, L. de Menezes","doi":"10.1109/WCNPS.2017.8252935","DOIUrl":null,"url":null,"abstract":"This work presents an estimation method for the calculation of the error between numerical and analytical solutions of the Laplace Equation. The study is performed by obtaining general estimates for the exact error of the numerical difference equation. The method is based on the polynomial approximation of the error using relative dimension simulations. The work is validated by comparison between the discrete solutions and numerical results, and with general problems.","PeriodicalId":293027,"journal":{"name":"2017 Workshop on Communication Networks and Power Systems (WCNPS)","volume":"4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Estimating the error between analytical and numerical finite difference solutions of laplace equation\",\"authors\":\"Alcyone César Pereira Silva, L. de Menezes\",\"doi\":\"10.1109/WCNPS.2017.8252935\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This work presents an estimation method for the calculation of the error between numerical and analytical solutions of the Laplace Equation. The study is performed by obtaining general estimates for the exact error of the numerical difference equation. The method is based on the polynomial approximation of the error using relative dimension simulations. The work is validated by comparison between the discrete solutions and numerical results, and with general problems.\",\"PeriodicalId\":293027,\"journal\":{\"name\":\"2017 Workshop on Communication Networks and Power Systems (WCNPS)\",\"volume\":\"4 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2017 Workshop on Communication Networks and Power Systems (WCNPS)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/WCNPS.2017.8252935\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2017 Workshop on Communication Networks and Power Systems (WCNPS)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/WCNPS.2017.8252935","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Estimating the error between analytical and numerical finite difference solutions of laplace equation
This work presents an estimation method for the calculation of the error between numerical and analytical solutions of the Laplace Equation. The study is performed by obtaining general estimates for the exact error of the numerical difference equation. The method is based on the polynomial approximation of the error using relative dimension simulations. The work is validated by comparison between the discrete solutions and numerical results, and with general problems.
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