A higher accuracy finite difference method for an elliptic equation of order four

Authors:
Tadeusz Styš
Affiliations:
Department of Mathematics, University of Botswana, Private Bag 0022, Gaborone, Botswana
Venue:
Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
Year:
2004

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Abstract

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 solve BHPEQ. The Module solve BHPEQ gives options either it implements the O(h4) convergent nine mesh points scheme or the O(h2) convergent standard five points scheme, when the finite difference approximation of Eq, (1) is considered.