Page 127 - Excel for Scientists and Engineers: Numerical Methods

104 EXCEL: NUMERICAL METHODS

Table 6-1. Some Formulas for Computing Derivatives
(For tables with equally spaced entries)
First derivative, using two points:
' Yi+l -Y;
Forward difference Yi =
h

Central difference

*
Backward difference y. = Yi - Yi-1
h
First derivative, using three points:

Forward difference

First derivative, using four points:
- y,+2 + 8Y,+, - 8Y,-I + YI-2
9
Central difference Y, = 12h
Second derivative, using three points:
Forward difference

,, y;+1 - 2Yi + Yi-I
Central difference Yi =
h2
yi - 2Yj-I + Yi-2
I,
Backward difference Yi =
h2
Second derivative, using four points:
-
2~, %+I + - x+3
'1
Forward difference Y, = h2
Second derivative, usingjbe points:
,, - yi+2 + l6~,+~ 30~; 16Yi-l - Yi-2
+
-
Central difference y. =
12h2
Third derivative, using four points
~j+3 - 3~;+2 + 3~i+l - Yi
Forward difference y. =
~~~
h3