MARCHING METHODS FOR ELLIPTIC PROBLEMS: PART 2

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Abstract
Further extensions are presented for the basic marching method for elliptic equations. The basic marching method is direct, that is, noniterative, but some of the most powerful techniques presented herein utilize it within rapidly converging iterative schemes. The solution techniques for the use of higher-order accuracy formulas are given, followed by the techniques for higher-order elliptic equations such as the biharmonic equation. Several techniques are given for extending the mesh size of the problem, thereby overcoming the inherent instability of the marching method.