{"title":"具有精确参数的三种六阶显式辛龙格-库塔-奈斯特罗姆方法","authors":"Mengjiao Pan , Jingjing Zhang , Shangyou Zhang","doi":"10.1016/j.rinam.2025.100568","DOIUrl":null,"url":null,"abstract":"<div><div>For separable Hamiltonian systems, we construct first ever three symplectic explicit Runge–Kutta-Nyström methods of six orders with exact parameters. We numerically and theoretically compare these three new exact methods with the only existing exact 6-th order symplectic explicit partitioned Runge–Kutta method and two approximate 6-th order symplectic explicit Runge–Kutta-Nyström methods. These new methods are more accurate and stable.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"26 ","pages":"Article 100568"},"PeriodicalIF":1.4000,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Three sixth-order explicit symplectic Runge–Kutta-Nystrom methods with exact parameters\",\"authors\":\"Mengjiao Pan , Jingjing Zhang , Shangyou Zhang\",\"doi\":\"10.1016/j.rinam.2025.100568\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>For separable Hamiltonian systems, we construct first ever three symplectic explicit Runge–Kutta-Nyström methods of six orders with exact parameters. We numerically and theoretically compare these three new exact methods with the only existing exact 6-th order symplectic explicit partitioned Runge–Kutta method and two approximate 6-th order symplectic explicit Runge–Kutta-Nyström methods. These new methods are more accurate and stable.</div></div>\",\"PeriodicalId\":36918,\"journal\":{\"name\":\"Results in Applied Mathematics\",\"volume\":\"26 \",\"pages\":\"Article 100568\"},\"PeriodicalIF\":1.4000,\"publicationDate\":\"2025-04-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Results in Applied Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2590037425000329\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Results in Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2590037425000329","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Three sixth-order explicit symplectic Runge–Kutta-Nystrom methods with exact parameters
For separable Hamiltonian systems, we construct first ever three symplectic explicit Runge–Kutta-Nyström methods of six orders with exact parameters. We numerically and theoretically compare these three new exact methods with the only existing exact 6-th order symplectic explicit partitioned Runge–Kutta method and two approximate 6-th order symplectic explicit Runge–Kutta-Nyström methods. These new methods are more accurate and stable.