Numerical Solution of the 2-Hessian Equation by a Newton�?¢�?�?��?�?�s Algorithm

[摘要] 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.

[关键词] Numerical solution;Boundary;Matrix;Periodic function