The elliptic Equation (1) with boundary value conditions either (2) or (3) is solved by an O(h4) convergent finite difference method combined with an implicit iterative method. The method is tested by examples of boundary value problems with use of the enclosed Mathematica module solveBHPEQ. The Module solveBHPEQ gives options either it implements the O(h~4) convergent nine mesh points scheme or the O(h~2) convergent standard five points scheme, when the finite difference approximation of Eq. (1) is considered.
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