Numerical Methods for Engine acin/About/Droid/uploads/Numerical%20Methods.pdf YouTube engineers 130/987 Use an initial guess of x = 0.5 and iterate until & ≤0.01%. Verify that the process is linearly convergent as described in Box 6.1. 6.2 Determine the highest real root of f(x) = 2x³- 11.7x² + 17.7x - 5 (a) Graphically. (b) Fixed-point iteration method (three iterations, x0 = 3). Note: Make certain that you develop a solution that converges on the root. (c) Newton-Raphson method (three iterations, x0 = 3). 286% 0.5 Use (a) mixed-point Iteration and (D) the Newton-Raphson method to determine a root of f(x) -0.9x² + 1.7x+ 2.5 using Xo -- = = 0.01%. 5. Perform the computation until & is less than ε, Also perform an error check of your final answer. 6.4 Determine the real roots of f(x) = -1 + 5.5x-4x² + 0.5x3: (a) graphically and (b) using the Newton-Raphson method to within & = 0.01%. 6.5 Employ the Newton-Raphson method to determine a real root for f(x) = −1 +5.5x-4x² + 0.5x³ using initial guesses of (a) 4.52 174 OPEN METHODS and (b) 4.54. Discuss and use graphical and analytical methods to ex- plain any peculiarities in your results. 6.6 Determine the lowest real root of f(x)=-12-21x+ 18x2 2.4x³: (a) graphically and (b) using the secant method to a value of ε, corresponding to three significant figures. 6.7 Locate the first positive root of f(x)= = sinx + cos(1 + x²) - 1 where x is in radians. Use four iterations of the secant method with Q Search Pick the best numerical technique, justify your choice and then use that technique to determine the root. Note that it is known that for positive initial guesses, all techniques except fixed-point iteration will eventually converge. Perform iterations until the approximate relative error falls below 2%. If you use a bracket- ing method, use initial guesses of x= O and x = 2. If you use the Newton-Raphson or the modified secant method, use an ini- tial guess of x = 0.7. If you use the secant method, use initial guesses of x-1= 0 and x = 2. 614 Ice (a) the Newton-Ranhson method and (h) the modified HAGESPRIES ENG (1) (2) Problem 6.5: Do the following (ignore textbook's instructions): i. Plot function using Matlab. Print this plot. ii. Find all three roots by Newton-Raphson Method. Write your own Matlab function, print the function, and indicate the answers. (Use error tolerance of 0.01%). iii. Use Matlab's roots function to verify your answer (no need to print). Use Newton-Raphson to estimate the root of f(x) = ex-x using x = 0 as an initial guess. Re-use the Matlab function from Prob. (1), print the code and indicate the answer. Also, use Excel Solver to verify your answer (print the cells that you used).
Numerical Methods for Engine acin/About/Droid/uploads/Numerical%20Methods.pdf YouTube engineers 130/987 Use an initial guess of x = 0.5 and iterate until & ≤0.01%. Verify that the process is linearly convergent as described in Box 6.1. 6.2 Determine the highest real root of f(x) = 2x³- 11.7x² + 17.7x - 5 (a) Graphically. (b) Fixed-point iteration method (three iterations, x0 = 3). Note: Make certain that you develop a solution that converges on the root. (c) Newton-Raphson method (three iterations, x0 = 3). 286% 0.5 Use (a) mixed-point Iteration and (D) the Newton-Raphson method to determine a root of f(x) -0.9x² + 1.7x+ 2.5 using Xo -- = = 0.01%. 5. Perform the computation until & is less than ε, Also perform an error check of your final answer. 6.4 Determine the real roots of f(x) = -1 + 5.5x-4x² + 0.5x3: (a) graphically and (b) using the Newton-Raphson method to within & = 0.01%. 6.5 Employ the Newton-Raphson method to determine a real root for f(x) = −1 +5.5x-4x² + 0.5x³ using initial guesses of (a) 4.52 174 OPEN METHODS and (b) 4.54. Discuss and use graphical and analytical methods to ex- plain any peculiarities in your results. 6.6 Determine the lowest real root of f(x)=-12-21x+ 18x2 2.4x³: (a) graphically and (b) using the secant method to a value of ε, corresponding to three significant figures. 6.7 Locate the first positive root of f(x)= = sinx + cos(1 + x²) - 1 where x is in radians. Use four iterations of the secant method with Q Search Pick the best numerical technique, justify your choice and then use that technique to determine the root. Note that it is known that for positive initial guesses, all techniques except fixed-point iteration will eventually converge. Perform iterations until the approximate relative error falls below 2%. If you use a bracket- ing method, use initial guesses of x= O and x = 2. If you use the Newton-Raphson or the modified secant method, use an ini- tial guess of x = 0.7. If you use the secant method, use initial guesses of x-1= 0 and x = 2. 614 Ice (a) the Newton-Ranhson method and (h) the modified HAGESPRIES ENG (1) (2) Problem 6.5: Do the following (ignore textbook's instructions): i. Plot function using Matlab. Print this plot. ii. Find all three roots by Newton-Raphson Method. Write your own Matlab function, print the function, and indicate the answers. (Use error tolerance of 0.01%). iii. Use Matlab's roots function to verify your answer (no need to print). Use Newton-Raphson to estimate the root of f(x) = ex-x using x = 0 as an initial guess. Re-use the Matlab function from Prob. (1), print the code and indicate the answer. Also, use Excel Solver to verify your answer (print the cells that you used).
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter1: Basic Modes Of Heat Transfer
Section: Chapter Questions
Problem 1.3DP
Related questions
Question
Problem 6.5
Transcribed Image Text:Numerical Methods for Engine
acin/About/Droid/uploads/Numerical%20Methods.pdf
YouTube
engineers
130/987
Use an initial guess of x = 0.5 and iterate until & ≤0.01%. Verify
that the process is linearly convergent as described in Box 6.1.
6.2 Determine the highest real root of
f(x) = 2x³- 11.7x² + 17.7x - 5
(a) Graphically.
(b) Fixed-point iteration method (three iterations, x0 = 3). Note: Make
certain that you develop a solution that converges on the root.
(c) Newton-Raphson method (three iterations, x0 = 3).
286%
0.5 Use (a) mixed-point Iteration and (D) the Newton-Raphson
method to determine a root of f(x)
-0.9x² + 1.7x+ 2.5 using
Xo
--
=
= 0.01%.
5. Perform the computation until & is less than ε,
Also perform an error check of your final answer.
6.4 Determine the real roots of f(x) = -1 + 5.5x-4x² + 0.5x3:
(a) graphically and (b) using the Newton-Raphson method to
within & = 0.01%.
6.5 Employ the Newton-Raphson method to determine a real root for
f(x) = −1 +5.5x-4x² + 0.5x³ using initial guesses of (a) 4.52
174
OPEN METHODS
and (b) 4.54. Discuss and use graphical and analytical methods to ex-
plain any peculiarities in your results.
6.6 Determine the lowest real root of f(x)=-12-21x+
18x2 2.4x³: (a) graphically and (b) using the secant method to a
value of ε, corresponding to three significant figures.
6.7 Locate the first positive root of
f(x)=
= sinx + cos(1 + x²) - 1
where x is in radians. Use four iterations of the secant method with
Q Search
Pick the best numerical technique, justify your choice and then
use that technique to determine the root. Note that it is known
that for positive initial guesses, all techniques except fixed-point
iteration will eventually converge. Perform iterations until the
approximate relative error falls below 2%. If you use a bracket-
ing method, use initial guesses of x= O and x = 2. If you use
the Newton-Raphson or the modified secant method, use an ini-
tial guess of x = 0.7. If you use the secant method, use initial
guesses of x-1= 0 and x = 2.
614 Ice (a) the Newton-Ranhson method and (h) the modified
HAGESPRIES
ENG
Transcribed Image Text:(1)
(2)
Problem 6.5: Do the following (ignore textbook's instructions):
i. Plot function using Matlab. Print this plot.
ii. Find all three roots by Newton-Raphson Method. Write your
own Matlab function, print the function, and indicate the
answers. (Use error tolerance of 0.01%).
iii. Use Matlab's roots function to verify your answer (no need to
print).
Use Newton-Raphson to estimate the root of f(x) = ex-x using x = 0 as an
initial guess. Re-use the Matlab function from Prob. (1), print the code and
indicate the answer. Also, use Excel Solver to verify your answer (print the
cells that you used).
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