关键词: 复蒙日－安培方程, 数值解, Dirichlet问题, Cartan-Hartogs域, Kaehler-Einstein度量, 二阶非线性常微分方程的两点边值问题

Abstract:

Monge-Ampere equation is a nonlinear equation with high degree, therefore to get its numerical solution is very difficult. This paper studies the numerical solution of Dirichlet problem of complex Monge-Amp`ere equation on Cartan-Hartogs domain of the fourth type. Firstly, this problem is reduced to the numberical solution of two-point boundary value problem of a nonlinear second-order ordinary differential equation. Secondly, the solution of the above Dirichlet's problem is given in explicit formula under the special case, this explicit formula can be used to check above numerical
solution.

Key words: Complex Monge-Ampere equation, Dirichlets problem,  Cartan-Hartogs domain,  Kaehler-Einstein metric, Two-Point boundary value problems