Two piecewise Hermite bicubic orthogonal spline collocation schemes are considered for the approximate solution of elliptic nonhomogeneous Dirichlet boundary value problems on rectangles. In the first scheme the nonhomogeneous Dirichlet boundary condition is approximated by means of the piecewise Hermite cubic interpolant, while the piecewise cubic interpolant at the boundary Gauss points is used in the second scheme. The piecewise Hermite bicubic interpolant of the exact solution of the boundary value problem is employed as a comparison function to show that the Hi-norm of the error for each scheme is O(h3).
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