Abstract:
We present a method to factorize a second order boundary value problem into a system of
uncoupled first order initial value problems, together with a nonlinear Riccati type equation
for functional operators. This factorization utilizes either the Neumann to Dirichlet (NtD) operator
or the Dirichlet to Neumann (DtN) operator, which satisfy a Riccati equation.This method can
be viewed as an infinite dimensional generalization of the block Gauss LU factorization.
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