(a) To obtain the root of the f(x)=x³-ln (x)-1 function using the simple one-point sequential method (fixed point iteration method) and (b) the secant method and (c) the Newton-Raphson method. For the fixed point iteration method, let x0 = 0.5 and the result is obtained in 8 iterations. The first estimate for the secant method is x0 = 0.1 and the second The predicted value is x1 = 0.2 and the result is obtained in 8 iterations. For the Newton-Raphson method, the initial predictive value is x0 0.1 and the result is obtained in 6 iterations.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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(a) To obtain the root of the
f (x) =x³-1n (x)-1 function using the
simple one-point sequential method
(fixed point iteration method) and
(b) the secant method and (c) the
Newton-Raphson method. For the
fixed point iteration method, let
хо
0.5 and the result is obtained
in 8 iterations.
The first estimate for the secant
method is x0 = 0.1 and the second
The predicted value is x1 = 0.2 and
the result is obtained in 8
iterations. For the Newton-Raphson
method, the initial predictive
value is x0
0.1 and the result is
obtained in 6 iterations.
Transcribed Image Text:(a) To obtain the root of the f (x) =x³-1n (x)-1 function using the simple one-point sequential method (fixed point iteration method) and (b) the secant method and (c) the Newton-Raphson method. For the fixed point iteration method, let хо 0.5 and the result is obtained in 8 iterations. The first estimate for the secant method is x0 = 0.1 and the second The predicted value is x1 = 0.2 and the result is obtained in 8 iterations. For the Newton-Raphson method, the initial predictive value is x0 0.1 and the result is obtained in 6 iterations.
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