{"title":"直接求解$z''(t)=g(t,z,z')$的改进龙格-库塔公式","authors":"Kasim Hussain, F. Ismail","doi":"10.12732/IJAM.V33I1.3","DOIUrl":null,"url":null,"abstract":"This paper deals with the derivation of an explicit two-stage thirdorder Improved Runge-Kutta Nyström (IRKNG) method for directly solving general second order ordinary differential equations (ODE). This method is twostep and the number of functions to be evaluated per step is less via comparsion to the existing RK methods. Numerical outcomes are offered to show the validity and competency of the newly IRKNG method as comparison with the general RKN and RK techniques. AMS Subject Classification: 65L05, 65l06","PeriodicalId":14365,"journal":{"name":"International journal of pure and applied mathematics","volume":"171 1","pages":"27"},"PeriodicalIF":0.0000,"publicationDate":"2020-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A NEW IMPROVED RUNGE-KUTTA FORMULA FOR DIRECTLY SOLVING $z''(t)=g(t,z,z')$\",\"authors\":\"Kasim Hussain, F. Ismail\",\"doi\":\"10.12732/IJAM.V33I1.3\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper deals with the derivation of an explicit two-stage thirdorder Improved Runge-Kutta Nyström (IRKNG) method for directly solving general second order ordinary differential equations (ODE). This method is twostep and the number of functions to be evaluated per step is less via comparsion to the existing RK methods. Numerical outcomes are offered to show the validity and competency of the newly IRKNG method as comparison with the general RKN and RK techniques. AMS Subject Classification: 65L05, 65l06\",\"PeriodicalId\":14365,\"journal\":{\"name\":\"International journal of pure and applied mathematics\",\"volume\":\"171 1\",\"pages\":\"27\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-02-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International journal of pure and applied mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.12732/IJAM.V33I1.3\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International journal of pure and applied mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.12732/IJAM.V33I1.3","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A NEW IMPROVED RUNGE-KUTTA FORMULA FOR DIRECTLY SOLVING $z''(t)=g(t,z,z')$
This paper deals with the derivation of an explicit two-stage thirdorder Improved Runge-Kutta Nyström (IRKNG) method for directly solving general second order ordinary differential equations (ODE). This method is twostep and the number of functions to be evaluated per step is less via comparsion to the existing RK methods. Numerical outcomes are offered to show the validity and competency of the newly IRKNG method as comparison with the general RKN and RK techniques. AMS Subject Classification: 65L05, 65l06
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