{"title":"优化的四阶龙格-库塔法","authors":"Xiong You, Xinmeng Yao, Xin Shu","doi":"10.1109/ICIC.2010.195","DOIUrl":null,"url":null,"abstract":"In this paper the order conditions for Runge-Kutta methods are presented based on Butcher's rooted tree theory. A new Runge-Kutta method of order four (MINRK4) is obtained by means of minimizing the error constant. The results of numerical experiments show the competence of the new method in accuracy and efficiency compared with some highly efficient codes in the literature.","PeriodicalId":176212,"journal":{"name":"2010 Third International Conference on Information and Computing","volume":"98 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-06-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"An Optimized Fourth Order Runge-Kutta Method\",\"authors\":\"Xiong You, Xinmeng Yao, Xin Shu\",\"doi\":\"10.1109/ICIC.2010.195\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper the order conditions for Runge-Kutta methods are presented based on Butcher's rooted tree theory. A new Runge-Kutta method of order four (MINRK4) is obtained by means of minimizing the error constant. The results of numerical experiments show the competence of the new method in accuracy and efficiency compared with some highly efficient codes in the literature.\",\"PeriodicalId\":176212,\"journal\":{\"name\":\"2010 Third International Conference on Information and Computing\",\"volume\":\"98 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2010-06-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2010 Third International Conference on Information and Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/ICIC.2010.195\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2010 Third International Conference on Information and Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICIC.2010.195","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
In this paper the order conditions for Runge-Kutta methods are presented based on Butcher's rooted tree theory. A new Runge-Kutta method of order four (MINRK4) is obtained by means of minimizing the error constant. The results of numerical experiments show the competence of the new method in accuracy and efficiency compared with some highly efficient codes in the literature.
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