一类复蒙日-安培方程Dirichlet问题数值解探讨

Research on Numerical Solution of Dirichlet Problem of Complex Monge-ampere Equation

蒙日-安培方程是高度非线性的偏微分方程,因此它的数值解非常困难.本文对第三类Cartan-Hartogs域上的复蒙日-安培方程Dirichlet问题数值解进行了探讨.首先,把该问题化为一个二阶非线性常微分方程的两点边值问题的数值解.其次,在一些特殊的情况下,得到了该方程的Dirichlet问题解的显表达式,它可以用来检验该问题的数值解.

Complex 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-Ampere equation on Cartan-Hartogs domain of the third 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.