Forward DifferenceΒΆ

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 None None None
\(h_i\) \(h_i \in \mathbb{R}^+\) None None None

Output Parameters

Parameter Type Constraint Description Remarks
\(\hat{Y}\) A data vector None First derivative of \(Y\) with respect to time \(t\) None

Single Steps using the Algorithm

References

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