Bisection Method: e- lnx f6) = e* - Ia x f(0) -e- In(0) = f1) =e- In(1) = 0.368 r(2) = e - In(2) --0.558 Remember that for Bisection Method, the roots will lie between opposite signs. Interval will lie between (1. 2) f(a) f(b) a+b fle) b-a 0.368 -1.2543 2.5752 2.5752 -0.558 0.558 0.558 2.7073 0.095 -0.9062 0.9936 2.64125 -1.2543 2.5752 2.7073 -0.095 2.095 -0.9062 -0.9062 2.9062 18998 0.9936 13.0604 • Continuing the iteration, you will have up to 19 iteration to get the difference of b-a becomes 0.05 and below
Bisection Method: e- lnx f6) = e* - Ia x f(0) -e- In(0) = f1) =e- In(1) = 0.368 r(2) = e - In(2) --0.558 Remember that for Bisection Method, the roots will lie between opposite signs. Interval will lie between (1. 2) f(a) f(b) a+b fle) b-a 0.368 -1.2543 2.5752 2.5752 -0.558 0.558 0.558 2.7073 0.095 -0.9062 0.9936 2.64125 -1.2543 2.5752 2.7073 -0.095 2.095 -0.9062 -0.9062 2.9062 18998 0.9936 13.0604 • Continuing the iteration, you will have up to 19 iteration to get the difference of b-a becomes 0.05 and below
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
With the informations provided below, continue to solve at least 15 iterations to satisfy the functions and answers what is asked through BISECTION METHOD
![Solution:
Bisection Method:
e- Inx
f(x) = e - Inx
• f(0) = e- - In(0) = 0
f(1) = e-- In(1) = 0.368
• f(2) = e-- In(2) = -0.558
Remember that for Bisection Method, the roots will lie between opposite signs.
Interval will lie between (1.2]
a +b
C
a
b
f(a)
f(b)
f(e)
b-a
1
0.368
-0.558
-0.55S
-0.095
-0.9062
0.9936
-1.2543
2.5752
1
2.095
-0.095
2
-1.2543
2.5752
-0.9062
-0.558
2.7073
2.9062
-0.9062
0.9936
2.5752
2.7073
2.64125
13.0604
1.8998
Continuing the iteration, you wil have up to 15 iteration to get the difference of b- a becomes 0.05 and below](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0678f50b-363a-45cf-8795-16bfe2a9cee7%2F3db6d7ea-cf9e-4980-bffb-a9501985aec2%2Fs7sfe4k_processed.png&w=3840&q=75)
Transcribed Image Text:Solution:
Bisection Method:
e- Inx
f(x) = e - Inx
• f(0) = e- - In(0) = 0
f(1) = e-- In(1) = 0.368
• f(2) = e-- In(2) = -0.558
Remember that for Bisection Method, the roots will lie between opposite signs.
Interval will lie between (1.2]
a +b
C
a
b
f(a)
f(b)
f(e)
b-a
1
0.368
-0.558
-0.55S
-0.095
-0.9062
0.9936
-1.2543
2.5752
1
2.095
-0.095
2
-1.2543
2.5752
-0.9062
-0.558
2.7073
2.9062
-0.9062
0.9936
2.5752
2.7073
2.64125
13.0604
1.8998
Continuing the iteration, you wil have up to 15 iteration to get the difference of b- a becomes 0.05 and below
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