Gaussian Spectral Rules for the Three-Point Second Differences: I. A Two-Point Positive Definite Problem in a Semi-Infinite Domain

Authors:
Vladimir Druskin;Leonid Knizhnerman
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
1999

Citing 0
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Abstract

We suggest an approach to grid optimization for a second order finite-difference scheme for elliptic equations. A model problem corresponding to the three-point finite-difference semidiscretization of the Laplace equation on a semi-infinite strip is considered. We relate the approximate boundary Neumann-to-Dirichlet map to a rational function and calculate steps of our finite-difference grid using the Padé--Chebyshev approximation of the inverse square root. It increases the convergence order of the Neumann-to-Dirichlet map from second to exponential without increasing the stencil of the finite-difference scheme and losing stability.