Forward Difference Operator/Examples

Examples of Forward Difference Operator

Value of $y_1$

The value of $y_1$ is given by:

$y_1 = y_0 + \Delta y_0$

where $\Delta y_0$ is the first forward difference of $y_0$.

Value of $y_2$

The value of $y_2$ is given by:

$y_2 = y_0 + 2 \Delta y_0 + \Delta^2 y_0$

where:

$\Delta y_0$ is the first forward difference of $y_0$

$\Delta^2 y_0$ is the second forward difference of $y_0$.

Value of $y_k$

The value of $y_k$ is given by:

$y_k = y_0 + \ds \sum_{s \mathop = 1}^k \dbinom k s \Delta^k y_0$

where $\Delta^k y_0$ is the $k$th forward difference of $y_0$.