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Results tagged with finite-differences
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user 36721
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Finite difference approximation
Given pairwise distinct real numbers $x_0,\dots,x_4$, one can approximate $f'(x_0)$ by a linear combination $a_0f(x_0)+\cdots+a_4f(x_4)$ so that
$$g_j'(x_0)=a_0g_j(x_0)+\cdots+a_4g_j(x_4)$$
for $g_j(x …
- 128k
2
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Change of variable formulas in discrete calculus?
$\newcommand\De\Delta$Elementarily: The relation $f=\De_h^{-1}g$ means that $f(x+h)-f(x)=g(x)$ for all $x$.
For a function $g$ and each real $r$, we know $f_r:=\De_1^{-1}g_r$, where $g_r(x):=g(rx)$, s …
- 128k