An efficient approach for the numerical solution of the Monge-Ampere equation

In this paper, we present a new method to compute the numerical solution of the elliptic Monge-Ampere equation. This method is based on solving a parabolic Monge-Ampere equation for the steady state solution. We study the problem of global existence, uniqueness, and convergence of the solution of the fully nonlinear parabolic PDE to the unique solution of the elliptic Monge-Ampere equation. Some numerical experiments are presented to show the convergence and the regularity of the numerical solution. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.