This preview shows page 1. Sign up to view the full content.
Unformatted text preview: 2.
f (x) = ex
∆x = .1
Approximate f (x) at x = 2 using forward diﬀerence
f (2) ∼ f (2 + .1) − f (2)
+ O (.1)
.1 f (2) ∼ e2.1 − e2
= 7.7711381
.1 Approximate f (x) at x = 2 using centered diﬀerence
f (2) ∼ f (2 + .1) − f (2 − .1)
+ O (.12)
.2 f (2) ∼ e2.1 − e1.9
= 7.40137735
.2 Approximate f (x) at x = 2 using second order three point
f (2) ∼ −f (2 + .2) + 4f (2 + .1) − 3f (2)
+ O (.12 )
.2 −e2.2 + 4e2.1 − 3e2
= 7.36248927
f (2) ∼
.2
Exact answer f (2) = e2 = 7.3890560989 . . . O (.1)
Forward
approximate 7.7711381
exact
7.3890560989
diﬀerence
.382082037
∼ .1 O (.12 )
Centered
7.40137735
7.3890560989
.01232125
∼ .12 O (.1)2
3point
7.36248927
7.3890560989
.0265668
∼ .12 Now use ∆x = .2 Approximate f (x) at x = 2 using forward diﬀerence
f (2) ∼ f (2 + .2) − f (2)
+ O (.2)
.2 f (2) ∼ e2.2 − e2
= 8.179787
.2 Approximate f (x) at x = 2 using centered diﬀerence
f (2) ∼ f (2 + .2) − f (2 − .2)
+ O (.22)
.4
293 ...
View
Full
Document
This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.
 Fall '08
 BELL,D

Click to edit the document details