Acta mathematica scientia,Series A ›› 2013, Vol. 33 ›› Issue (4): 646-654.

• Articles • Previous Articles     Next Articles

Research on Numerical Solution of Dirichlet Problem of Complex Monge-Amp`ere Equation (IV)

 YAN Wei-Ping   

  1. School of Mathematical Science, Capital Normal University, Beijing 100048
  • Received:2012-02-07 Revised:2013-01-13 Online:2013-08-25 Published:2013-08-25
  • Supported by:

    国家自然科学基金(11071171, 11171285)资助.

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

CLC Number: 

  • 32C17
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