# Forward Difference¶

The basic formula for computing the Forward Difference derivative at the point $$t_i$$ is stated as follows:

$Y(t_i)' = \frac{Y(t_i+h_i) - Y(t_i)}{h_i}$

where $$Y(t_i)$$ is the function value at time point $$t_i$$, $$Y'(t_i)$$ is the first derivative at time point $$t_i$$, $$h_i$$ is the step size between the point $$t_i$$ and the next time point.

Input Parameters

Parameter Type Constraint Description Remarks
$$Y$$ A continuous function or a data vector
$$h_i$$ $$h_i \in \mathbb{R}^+$$

Output Parameters

Parameter Type Constraint Description Remarks
$$\hat{Y}$$ A data vector   First derivative of $$Y$$ with respect to time $$t$$

Single Steps using the Algorithm

References

• R. L. Burden and J. D. Faires, Numerical Analysis, Fifth Edition, PWS Publishing Co. Boston, MA, 1993.