{"title":"用同伦分析方法求解多种Lotka-Volterra方程","authors":"A. Bataineh, M. Noorani, I. Hashim","doi":"10.1155/2008/816787","DOIUrl":null,"url":null,"abstract":"The time evolution of the multispecies Lotka-Volterra system is investigated by the homotopy analysis method (HAM). The continuous solution for the nonlinear system is given, which provides a convenient and straightforward approach to calculate the dynamics of the system. The HAM continuous solution generated by polynomial base functions is of comparable accuracy to the purely numerical fourth-order Runge-Kutta method. The convergence theorem for the three-dimensional case is also given.","PeriodicalId":30100,"journal":{"name":"Differential Equations and Nonlinear Mechanics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2008-07-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1155/2008/816787","citationCount":"15","resultStr":"{\"title\":\"Series solution of the multispecies Lotka-Volterra equations by means of the homotopy analysis method\",\"authors\":\"A. Bataineh, M. Noorani, I. Hashim\",\"doi\":\"10.1155/2008/816787\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The time evolution of the multispecies Lotka-Volterra system is investigated by the homotopy analysis method (HAM). The continuous solution for the nonlinear system is given, which provides a convenient and straightforward approach to calculate the dynamics of the system. The HAM continuous solution generated by polynomial base functions is of comparable accuracy to the purely numerical fourth-order Runge-Kutta method. The convergence theorem for the three-dimensional case is also given.\",\"PeriodicalId\":30100,\"journal\":{\"name\":\"Differential Equations and Nonlinear Mechanics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2008-07-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1155/2008/816787\",\"citationCount\":\"15\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Differential Equations and Nonlinear Mechanics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1155/2008/816787\",\"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/10.1155/2008/816787","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Series solution of the multispecies Lotka-Volterra equations by means of the homotopy analysis method
The time evolution of the multispecies Lotka-Volterra system is investigated by the homotopy analysis method (HAM). The continuous solution for the nonlinear system is given, which provides a convenient and straightforward approach to calculate the dynamics of the system. The HAM continuous solution generated by polynomial base functions is of comparable accuracy to the purely numerical fourth-order Runge-Kutta method. The convergence theorem for the three-dimensional case is also given.
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