{"title":"常微分方程数值解的插值","authors":"M. Gordon, L. Shampine","doi":"10.1145/800182.810378","DOIUrl":null,"url":null,"abstract":"Methods like the Runge-Kutta family for the solution of ordinary differential equations produce approximate solutions only at mesh points. The efficiency of such methods is greatly reduced if the user requests output too frequently. This paper justifies interpolating to resolve this difficulty. In addition the use of interpolation to approximate the derivatives of the solution is justified","PeriodicalId":204185,"journal":{"name":"ACM '74","volume":"68 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"8","resultStr":"{\"title\":\"Interpolating numerical solutions of ordinary differential equations\",\"authors\":\"M. Gordon, L. Shampine\",\"doi\":\"10.1145/800182.810378\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Methods like the Runge-Kutta family for the solution of ordinary differential equations produce approximate solutions only at mesh points. The efficiency of such methods is greatly reduced if the user requests output too frequently. This paper justifies interpolating to resolve this difficulty. In addition the use of interpolation to approximate the derivatives of the solution is justified\",\"PeriodicalId\":204185,\"journal\":{\"name\":\"ACM '74\",\"volume\":\"68 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACM '74\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/800182.810378\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM '74","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/800182.810378","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Interpolating numerical solutions of ordinary differential equations
Methods like the Runge-Kutta family for the solution of ordinary differential equations produce approximate solutions only at mesh points. The efficiency of such methods is greatly reduced if the user requests output too frequently. This paper justifies interpolating to resolve this difficulty. In addition the use of interpolation to approximate the derivatives of the solution is justified