{"title":"显著性算法:在偏微分方程中的应用","authors":"R. Bivins, N. Metropolis","doi":"10.1109/ARITH.1975.6156973","DOIUrl":null,"url":null,"abstract":"The methods of significance arithmetic are applied to the numerical solution of a nonlinear partial differential equation. Our approach permits the use of initial values having imprecision considerably greater than that of rounding error; moreover, the intermediate and final quantities are monitored so that at any stage the precision of such quantities is available. An algorithm is found that represents faithfully the solution to a difference equation approximation to Burgers' equation.","PeriodicalId":360742,"journal":{"name":"1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)","volume":"14 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1975-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Significance arithmetic: Application to a partial differential equation\",\"authors\":\"R. Bivins, N. Metropolis\",\"doi\":\"10.1109/ARITH.1975.6156973\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The methods of significance arithmetic are applied to the numerical solution of a nonlinear partial differential equation. Our approach permits the use of initial values having imprecision considerably greater than that of rounding error; moreover, the intermediate and final quantities are monitored so that at any stage the precision of such quantities is available. An algorithm is found that represents faithfully the solution to a difference equation approximation to Burgers' equation.\",\"PeriodicalId\":360742,\"journal\":{\"name\":\"1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)\",\"volume\":\"14 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1975-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ARITH.1975.6156973\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"1975 IEEE 3rd Symposium on Computer Arithmetic (ARITH)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ARITH.1975.6156973","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Significance arithmetic: Application to a partial differential equation
The methods of significance arithmetic are applied to the numerical solution of a nonlinear partial differential equation. Our approach permits the use of initial values having imprecision considerably greater than that of rounding error; moreover, the intermediate and final quantities are monitored so that at any stage the precision of such quantities is available. An algorithm is found that represents faithfully the solution to a difference equation approximation to Burgers' equation.
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