Modelling PDEs - extension

The method of finite differences for second order derivatives

In one of the tutorials we give an expression for calculating second order derivatives using the finite difference method:

\begin{equation} \frac{\mathrm{d} ^2f}{\mathrm{d} x^2} \simeq \frac{f(x+h)-2f(x)+f(x-h)}{h^2}. \end{equation}

Using the fact that a second derivative is, by definition, a derivative of a derivative, and by applying the central difference method three times, derive this expression.

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