I have a Monge-Ampere-type PDE I wish to solve using a finite difference method:
$$(1-u_{xx})(1-u_{yy}) -u_{xy}^2 = f(x,y).$$
Is there generally a preferred method for linearising the system after discretisation? I've seen Newton's method is quite commonly used, but I guess working out the Jacobian could be quite expensive and your initial guess would have to be good. Many thanks.