Factorization of second-order elliptic boundary value problems by dynamic programming.

Abstract

We present a method to factorize a second-order boundary value problem in a cylindrical domain in a system of uncoupled first-order initial value problems, together with a nonlinear Riccati-type equation for functional operators. This uncoupling is obtained by a space invariant embedding technique along the axis of the cylinder. This method can be viewed as an infinite-dimensional generalization of the block Gauss LU factorization.