A research into the numerical method of Dirichlet's problem of complex Monge-Ampere equation on Cartan-Hartogs domain of the third type

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:339

Article

Yin, Weiping³  Yin, Xiaolan^1,2 

[1] Chinese Acad Sci, Inst Software, Technol Ctr Software Engn, Beijing 100080, Peoples R China

[2] Chinese Acad Sci, Grad Univ, Beijing 100049, Peoples R China

[3] Capital Normal Univ, Sch Math Sci, Beijing 100037, Peoples R China

关键词: complex Monge-Ampere equation;    Dirichlet's problem;    Cartan-Hartogs domain;    Kaehler-Einstein metric;   

DOI  :  10.1016/j.jmaa.2007.07.005

来源: Elsevier

【 摘 要 】

Monge-Ampere equation is a nonlinear equation with high degree, therefore its numerical solution is very important and very difficult. In present paper the numerical method of Dirichlet's problem of Monge-Ampere equation on Cartan-Hartogs domain of the third type is discussed by using the analytic method. Firstly, the Monge-Ampere equation is reduced to the nonlinear ordinary differential equation, then the numerical method of the Dirichlet problem of Monge-Ampere equation becomes the numerical method of two point boundary value problem of the nonlinear ordinary differential equation. Secondly, the solution of the Dirichlet problem is given in explicit formula under the special case, which can be used to check the numerical solution of the Dirichlet problem. (c) 2007 Elsevier Inc. All rights reserved.

【 授权许可】

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