Affiliation:
1. Department of Applied Mathematics, University of Colorado , Boulder, CO 80309, USA
Abstract
Abstract
It was recently found that finite difference (FD) formulas become remarkably accurate when approximating derivatives of analytic functions $f(z)$ in the complex $z=x+\text{i}y$ plane. On unit-spaced grids in the $x,y$-plane, the FD weights decrease to zero with the distance to the stencil center at a rate similar to that of a Gaussian, typically falling below the level of double precision accuracy $\mathcal{O}(10^{-16})$ already about four node spacings away from the center point. We follow up on these observations here by analyzing and illustrating the features of such FD stencils in their infinite-order accurate limit (for traditional FD approximations known as their pseudospectral limit).
Publisher
Oxford University Press (OUP)
Subject
Applied Mathematics,Computational Mathematics,General Mathematics
Cited by
3 articles.
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