Three-point finite-difference schemes, Padé and the spectral Galerkin method. I. One-sided impedance approximation |
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Authors: | Vladimir Druskin Shari Moskow. |
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Affiliation: | Schlumberger-Doll Research, Old Quarry Rd, Ridgefield, Connecticut 06877 ; Department of Mathematics, University of Florida, 358 Little Hall, P.O. Box 118105, Gainesville, Florida 32611-8105 |
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Abstract: | A method for calculating special grid placement for three-point schemes which yields exponential superconvergence of the Neumann to Dirichlet map has been suggested earlier. Here we show that such a grid placement can yield impedance which is equivalent to that of a spectral Galerkin method, or more generally to that of a spectral Galerkin-Petrov method. In fact we show that for every stable Galerkin-Petrov method there is a three-point scheme which yields the same solution at the boundary. We discuss the application of this result to partial differential equations and give numerical examples. We also show equivalence at one corner of a two-dimensional optimal grid with a spectral Galerkin method. |
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Keywords: | Second order scheme exponential superconvergence pseudospectral Galerkin-Petrov rational approximations |
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