{"title":"常微分方程的数值方法:早期","authors":"J. Butcher","doi":"10.1142/9789812836267_0003","DOIUrl":null,"url":null,"abstract":"Systems of ordinary and/or partial differential equations form the basis for nearly all mathematical models used in the physical, social and engineering sciences. Most of the equations that arise cannot be solved \"by hand\" and require the use of numerical methods to obtain solutions. The focus of the Math 269 series of courses is on the numerical methods used to create approximate solutions of systems of ordinary and partial differential equations.","PeriodicalId":412573,"journal":{"name":"The Birth of Numerical Analysis","volume":"78 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Numerical methods for ordinary differential equations: early days\",\"authors\":\"J. Butcher\",\"doi\":\"10.1142/9789812836267_0003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Systems of ordinary and/or partial differential equations form the basis for nearly all mathematical models used in the physical, social and engineering sciences. Most of the equations that arise cannot be solved \\\"by hand\\\" and require the use of numerical methods to obtain solutions. The focus of the Math 269 series of courses is on the numerical methods used to create approximate solutions of systems of ordinary and partial differential equations.\",\"PeriodicalId\":412573,\"journal\":{\"name\":\"The Birth of Numerical Analysis\",\"volume\":\"78 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The Birth of Numerical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/9789812836267_0003\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The Birth of Numerical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/9789812836267_0003","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Numerical methods for ordinary differential equations: early days
Systems of ordinary and/or partial differential equations form the basis for nearly all mathematical models used in the physical, social and engineering sciences. Most of the equations that arise cannot be solved "by hand" and require the use of numerical methods to obtain solutions. The focus of the Math 269 series of courses is on the numerical methods used to create approximate solutions of systems of ordinary and partial differential equations.