Journal de mathématiques appliquées et computationnelles

Numerical Solution of the 2-Hessian Equation by a Newton’s Algorithm

Abstract

Haj EA, Khalil H and Hossein M

The elliptic 2-Hessian equation is a fully nonlinear partial differential equation that is related, for example, to intrinsic curvature for three dimensional manifolds. We solve numerically this equation with periodic boundary condition and with Dirichlet boundary condition using a Newton’s algorithm. We verify numerically, by introducing finite difference schemes, the convergence of the algorithm which is obtained in few iterations.