{"title":"用同伦分析法直接解-阶ivp","authors":"A. Bataineh, M. Noorani, I. Hashim","doi":"10.1155/2009/842094","DOIUrl":null,"url":null,"abstract":"Direct solution of a class of -order initial value problems (IVPs) is considered based on the homotopy analysis method (HAM). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of the series solutions. The HAM gives approximate analytical solutions which are of comparable accuracy to the seven- and eight-order Runge-Kutta method (RK78).","PeriodicalId":30100,"journal":{"name":"Differential Equations and Nonlinear Mechanics","volume":"2009 1","pages":"842094"},"PeriodicalIF":0.0000,"publicationDate":"2009-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2009/842094","citationCount":"12","resultStr":"{\"title\":\"Direct Solution of -Order IVPs by Homotopy Analysis Method\",\"authors\":\"A. Bataineh, M. Noorani, I. Hashim\",\"doi\":\"10.1155/2009/842094\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Direct solution of a class of -order initial value problems (IVPs) is considered based on the homotopy analysis method (HAM). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of the series solutions. The HAM gives approximate analytical solutions which are of comparable accuracy to the seven- and eight-order Runge-Kutta method (RK78).\",\"PeriodicalId\":30100,\"journal\":{\"name\":\"Differential Equations and Nonlinear Mechanics\",\"volume\":\"2009 1\",\"pages\":\"842094\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-08-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1155/2009/842094\",\"citationCount\":\"12\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Equations and Nonlinear Mechanics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/2009/842094\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Differential Equations and Nonlinear Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1155/2009/842094","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Direct Solution of -Order IVPs by Homotopy Analysis Method
Direct solution of a class of -order initial value problems (IVPs) is considered based on the homotopy analysis method (HAM). The HAM solutions contain an auxiliary parameter which provides a convenient way of controlling the convergence region of the series solutions. The HAM gives approximate analytical solutions which are of comparable accuracy to the seven- and eight-order Runge-Kutta method (RK78).
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