A research into the numerical method of Dirichlet’s problem of complex Monge–Ampère equation on Cartan–Hartogs domain of the third type

Monge–Ampère 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–Ampère equation on Cartan–Hartogs domain of the third type is discussed by using the analytic method. Firstly, the Monge–Ampère equation is reduced to the nonlinear ordinary differential equation, then the numerical method of the Dirichlet problem of Monge–Ampère 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. © 2007 Elsevier Inc. All rights reserved.