$$ \newcommand{\uex}{{u_{\small\mbox{e}}}} \newcommand{\Aex}{{A_{\small\mbox{e}}}} \newcommand{\half}{\frac{1}{2}} \newcommand{\tp}{\thinspace .} \newcommand{\Oof}[1]{\mathcal{O}(#1)} \newcommand{\dfc}{\alpha} % diffusion coefficient $$

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The mesh Fourier number

$$ F = \dfc\frac{\Delta t}{\Delta x^2} $$

Observe.

There is only one parameter, \( F \), in the discrete model: \( F \) lumps mesh parameters \( \Delta t \) and \( \Delta x \) with the only physical parameter, the diffusion coefficient \( \dfc \). The value \( F \) and the smoothness of \( I(x) \) govern the quality of the numerical solution.

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