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Abstract : |
Singular terms in di#erential equations pose severe challenges for numerical approximations on regular grids. Regularization of the singularities is a very useful technique for their representation on the grid. We analyze such techniques for the practically preferred case of narrow support of the regularizations, extending our earlier results for wider support. The analysis also generalizes existing theory for one dimensional problems to multi dimensions. New high order multi dimensional techniques for di#erential equations and numerical quadrature are introduced based on the analysis and numerical results are presented. We also show that the common use of distance functions to extend one dimensional regularization to higher dimensions may produce O(1) errors. 1, |
