Iterative methods for k-Hessian equations
Numerical Analysis
2018-08-27 v3
Abstract
On a domain of the n-dimensional Euclidean space, and for an integer k=1,...,n, the k-Hessian equations are fully nonlinear elliptic equations for k >1 and consist of the Poisson equation for k=1 and the Monge-Ampere equation for k=n. We analyze for smooth non degenerate solutions a 9-point finite difference scheme. We prove that the discrete scheme has a locally unique solution with a quadratic convergence rate. In addition we propose new iterative methods which are numerically shown to work for non smooth solutions. A connection of the latter with a popular Gauss-Seidel method for the Monge-Ampere equation is established and new Gauss-Seidel type iterative methods for 2-Hessian equations are introduced.
Cite
@article{arxiv.1406.5366,
title = {Iterative methods for k-Hessian equations},
author = {Gerard Awanou},
journal= {arXiv preprint arXiv:1406.5366},
year = {2018}
}