Two piecewise Hermite bicubic orthogonal spline collocation schemes are considered for the approximate solution of elliptic, self-adjoint, nonhomogeneous Dirichlet boundary value problems on rectangles. In the rst scheme, the nonhomogeneous Dirichlet boundary condition is approximated by means of the piecewise Hermite cubic interpolant, while the piecewise cubic interpolant at the boundary Gaus...