Multimediální učebnice

Slovník pojmů

Finite differences

Finite differences are used to replace the value of a derivative in such situation, when the derivative cannot be evaluated. The derivative of the function f in the point x determines the tangent direction of a function in a given point (black line in Figure). This direction can be approximated exploiting the red rectangle as

Differentiation

f_{c}^{'} (x) \frac{f (x + h) - f (x - h)}{2 h}

If the point x is in the middle of the interval then we speak about the central differentiation. Red line and black one seem to be very similar.

Except of the central differentiation, the forward differentiation (dark-yellow rectangle)

f_{F}^{'} (x) = \frac{f (x + h) - f (x)}{2 h}

and the backward differentiation (cyan triangle)

f_{B}^{'} (x) = \frac{f (x) - f (x - h)}{2 h}

exist. Nevertheless, the difference between the dark-yellow line and black one (or a cyan line and black one) is more significant than in the case of the central differentiation.

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