2nd Level
Numerical Analysis
Sheet No.: 4
Title: Bisection Method
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Textbook: Numerical Methods for Engineers by: Steven C. Chapra, Raymond P.
Canal. McGraw-Hill.
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By using the bisection method, find one root to the following equations
with an error less than 0.05% :
1. 𝒇(𝒙) = 𝒙𝟑 − 𝟑𝒙 – 𝟓 in the interval [2,3].
2. 𝒇(𝒙) = 𝒙 – 𝒄𝒐𝒔(𝒙) in the interval [0,1].
3. 𝒇(𝒙) = 𝟑𝒙 – 𝒆𝒙 in the interval [0,1].
Extra Problems:
(2) Exercise of Chapter 5 p.139 numbers; 1(c), 2(b), 3(b), 14, 15
1
X1 Ve Xu ve Xp Hayat a Preset pre
Preset
too
2 3 2.5
2 2.5 2.25 11 2.25 2.5 100 11 Not
2.25
2 25 a 2.5 2.375 2.375,325 100 5.26
2.25 2.375 2.3125 2.7
2.25 2.3125 2.28125 1.36
2.25 2.28125 2.265625 0.68
2.265625 2.28125 2 2734375 0.34010
2 2734375 2.28125 2.27734375 0.179
2.27734375 2.28125 2.279296875 0.08
2.27734375 2.279296875 2.278320313 so 04010 Locos
Preset pre
Xp Xiyu a
present
too Radin assail
Xu tve Xi ve
0 I 0.5
0.5 I 0.75 33.333010
0.5 0.75 0.625 20
0.625 0.75 0.6875 9.09101
0.6875 0.75 0.71875 4.34801
0.71875 0.75 0.73438 2.12801
0.73438 0.75 0.74219 1.05301
0.73438 0.74219 0.73828 0.52901
0.73828 0.74219 0.74023 0.26401
0.73828 0.74023 0.73926 t 0.13201
0.73828 0.73926 0.73877 0.066010
0.73877 0.73926 0.73901 0.03301 0.05
X1 Ve Xu ve Xp Hayat a Preset pre
Preset
too
o 7 0.5
0.5 I 0.75 33.33010
0.5 0.75 0.625 1 20
0.5 0.625 0.5625 as 11.11010
0.5625 0.625 0.59375 5.263
0.59375 0.625 0.60938 2.56401
0.60938 0.625 0.61719 1.266010
0.61719 0.625 0.62109 0.629
0.61719 0.62109 0.61914 0.31501
0.61719 0.61914 0.61816 0.158
0.61816 0.61914 0.61865 0.079
0.61865 0.61914 0.61890 0.039 to Loosolo
