{"title":"高阶非线性方程解及其动力学行为","authors":"Sabir Yasin, Amir Naseem","doi":"10.30538/psrp-oma2018.0026","DOIUrl":null,"url":null,"abstract":"In this report we present new sixth order iterative methods for solving non-linear equations. The derivation of these methods is purely based on variational iteration technique. To check the validity and efficiency we compare of methods with Newton’s method, Ostrowski’s method, Traub’s method and modified Halleys’s method by solving some test examples. Numerical results shows that our developed methods are more effective. Finally, we compare polynomigraphs of our developed methods with Newton’s method, Ostrowski’s method, Traub’s method and modified Halleys’s method. Mathematics Subject Classification: 37F50.","PeriodicalId":52741,"journal":{"name":"Open Journal of Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2018-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Higher Order Nonlinear Equation Solvers and their Dynamical Behavior\",\"authors\":\"Sabir Yasin, Amir Naseem\",\"doi\":\"10.30538/psrp-oma2018.0026\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this report we present new sixth order iterative methods for solving non-linear equations. The derivation of these methods is purely based on variational iteration technique. To check the validity and efficiency we compare of methods with Newton’s method, Ostrowski’s method, Traub’s method and modified Halleys’s method by solving some test examples. Numerical results shows that our developed methods are more effective. Finally, we compare polynomigraphs of our developed methods with Newton’s method, Ostrowski’s method, Traub’s method and modified Halleys’s method. Mathematics Subject Classification: 37F50.\",\"PeriodicalId\":52741,\"journal\":{\"name\":\"Open Journal of Mathematical Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-12-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Open Journal of Mathematical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.30538/psrp-oma2018.0026\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Open Journal of Mathematical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.30538/psrp-oma2018.0026","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Higher Order Nonlinear Equation Solvers and their Dynamical Behavior
In this report we present new sixth order iterative methods for solving non-linear equations. The derivation of these methods is purely based on variational iteration technique. To check the validity and efficiency we compare of methods with Newton’s method, Ostrowski’s method, Traub’s method and modified Halleys’s method by solving some test examples. Numerical results shows that our developed methods are more effective. Finally, we compare polynomigraphs of our developed methods with Newton’s method, Ostrowski’s method, Traub’s method and modified Halleys’s method. Mathematics Subject Classification: 37F50.