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The general form of Poisson's equation for any field component &psi;(<b>r</b>) can be expressed as:

<math> \nablafrac{\partial^2 \psi(}{\mathbfpartial x^2} + \frac{r\partial^2\psi}) = {\partial y^2} + \frac{\partial^2\psi}{\partial xz^2} = -f(\mathbf{r}) </math> The second derivative of &psi; with respect to the coordinate x can be approximated by the second-order difference: <math> \frac{\partial^2\psi\mathbf{r}}{\partial x^2} \approx \frac{\psi(x+\Delta x,y,z)-2\psi(x,y,z)+\psi(x-\Delta x,y,z)}{(\Delta x)^2} </math>