 
Summary: PSEUDO TIME CONTINUATION AND TIME MARCHING
METHODS FOR MONGEAMP`ERE TYPE EQUATIONS
GERARD AWANOU
Abstract. We discuss the performance of three numerical methods for the fully
nonlinear MongeAmp`ere equation. The first two are pseudo time continuation
methods while the third is a pure pseudo time marching algorithm. The pseudo
time continuation methods are shown to converge for smooth data on a uniformly
convex domain. We give numerical evidence that they perform well for the non
degenerate MongeAmp`ere equation. The pseudo time marching method applies in
principle to any nonlinear equation. Numerical results with this approach for the
degenerate MongeAmp`ere equation are given as well as for the Pucci and Gauss
curvature equations.
1. Introduction
We are interested in numerical solutions of equations of type
(1.1) F(x, u(x), Du(x), D2
u(x)) = 0,
on a convex bounded domain of Rn
with boundary and Dirichlet boundary con
ditions u = g and F real valued. Here u is a real valued function and Du(x), D2
u(x)
