{"title":"用NewtonÃⅱÂÂs算法求解2-Hessian方程","authors":"Haj Ea, H. Khalil, M. Hossein","doi":"10.4172/21689679.1000393","DOIUrl":null,"url":null,"abstract":"The elliptic 2-Hessian equation is a fully nonlinear partial differential equation that is related, for example, to intrinsic curvature for three dimensional manifolds. We solve numerically this equation with periodic boundary condition and with Dirichlet boundary condition using a Newton’s algorithm. We verify numerically, by introducing finite difference schemes, the convergence of the algorithm which is obtained in few iterations.","PeriodicalId":15007,"journal":{"name":"Journal of Applied and Computational Mathematics","volume":"1 1","pages":"1-3"},"PeriodicalIF":0.0000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Numerical Solution of the 2-Hessian Equation by a NewtonâÂÂs Algorithm\",\"authors\":\"Haj Ea, H. Khalil, M. Hossein\",\"doi\":\"10.4172/21689679.1000393\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The elliptic 2-Hessian equation is a fully nonlinear partial differential equation that is related, for example, to intrinsic curvature for three dimensional manifolds. We solve numerically this equation with periodic boundary condition and with Dirichlet boundary condition using a Newton’s algorithm. We verify numerically, by introducing finite difference schemes, the convergence of the algorithm which is obtained in few iterations.\",\"PeriodicalId\":15007,\"journal\":{\"name\":\"Journal of Applied and Computational Mathematics\",\"volume\":\"1 1\",\"pages\":\"1-3\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Applied and Computational Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4172/21689679.1000393\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Computational Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4172/21689679.1000393","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Numerical Solution of the 2-Hessian Equation by a NewtonâÂÂs Algorithm
The elliptic 2-Hessian equation is a fully nonlinear partial differential equation that is related, for example, to intrinsic curvature for three dimensional manifolds. We solve numerically this equation with periodic boundary condition and with Dirichlet boundary condition using a Newton’s algorithm. We verify numerically, by introducing finite difference schemes, the convergence of the algorithm which is obtained in few iterations.
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