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Referring to the discretization of derivatives by Finite differences, and its applications to numerical solutions of partial differential equations.

7
votes
This paper, Generation of Finite Difference Formulas on Arbitrarily Spaced Grids, by Bengt Fornberg, provides Pseudo-Code for the... well... the title is a bit of a give-away. If you pack it into a l …
answered Apr 3 '12 by Pedro
6
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If you want to increase the accuracy of a finite difference scheme, you can always try increasing the degree of your stencil. On equidistant points, though, this can lead to numerical instabilities. T …
answered May 23 '12 by Pedro
26
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The problem with equispaced points is that the interpolation error polynomial, i.e. $$ f(x) - P_n(x) = \frac{f^{(n+1)}(\xi)}{(n+1)!} \prod_{i=0}^n (x - x_i),\quad \xi\in[x_0,x_n] $$ behaves differen …
answered Mar 26 '13 by Pedro