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   13:15 -- 14:00  Sean Settle (Seoul National University, Korea)
                  ``A systematic framework for high-order finite difference 
                    compact schemes''


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We derive high-order compact schemes for the Poisson equation in one 
and two dimensions. For 1D problems, the derivation is of arbitrary
even-order in theory and upt to 20th-order in 64-bit IEEE arithmetic.
For 2D problems, we derive up to tenth-order compact schemes.