2.3.2 Discretization in space by finite differences

Finite difference methods:

Restriction: sampling
Reconstruction: interpolation (by polynomials)
Derivatives become finite differences

``Sampling'' means: to go from continuous values of $\bgroup\color{DEFcolor}$\rho(x)$\egroup$ to a discrete set of values $\bgroup\color{DEFcolor}$\rho_i$\egroup$ for a grid with $\bgroup\color{DEFcolor}$x_i = \Delta x i + x_0$\egroup$ we set

$\begin{displaymath} \rho_i = \rho \left( x_i \right) \enspace . \end{displaymath}$

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