Use fixed-point iteration and graphical method to determine a root of f(x) = -x² + 1.8x+2.5 using x = 5. Perform the computation until & is less than & = 0.05%
Use fixed-point iteration and graphical method to determine a root of f(x) = -x² + 1.8x+2.5 using x = 5. Perform the computation until & is less than & = 0.05%
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Formulas:
xi+1=g(xi)
ℇa=|xi+1-xi / xi+1 | 100%
Transcribed Image Text:Use fixed-point iteration and graphical method to determine a root of
f(x) = -x² + 1.8x+2.5 using x = 5.
Perform the computation until & is less than & = 0.05%
Transcribed Image Text:●
Simple Fixed-point Method
Example 1: Use simple fixed-point iteration to locate the root
of f(x) = e¯x - x
● Solution: The function can be
separated
directly
and
expressed in the form of
Eqn. I as
Xj+1
= e-xi
Starting with an initial guess of x = 0, this iterative
equation can be applied to compute:
&a (%)
i
O
1
2
3
4
Each iteration brings the estimate 8
closer to the true value of the root: 9
0.56714329.
10
O
Xi
1.000000
0.367879
0.692201
0.500473
0.606244
0.545396
0.579612
0.560115
0.571143
0.564879
E.B.P.
100.0
171.8
46.9
38.3
17.4
11.2
5.90
3.48
1.93
1.11
&t (%)
100.0
76.3
35.1
22.1
11.8
6.89
3.83
2.20
1.24
0.705
0.399
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