(2) Calculate by hand three iterations of the Golden-Section Search algorithm toapproximate the maximum of f(x) = -0.1x² - ex. Use an initial bracket of XL =0 and xu = 3. Show work, and for each iteration indicate the value of Xopt.

Answered: Image /qna-images/answer/4264e5b7-901e-4fe2-9c8a-d24b9eee35ec.jpg

Answered: (2) Calculate by hand three iterations…

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.

Chapter4: Numerical Analysis Of Heat Conduction

Section: Chapter Questions

Problem 4.7P

See similar textbooks

Similar questions

I need the answer as soon as possible
f(x)=-0.9x? +1.7x+2.5 Calculate the root of the function given below: a) by Newton-Raphson method b) by simple fixed-point iteration method. (f(x)=0) Use x, = 5 as the starting value for both methods. Use the approximate relative error criterion of 0.1% to stop iterations.
x^2-5x^(1/3)+1=0 Has a root between 2 and 2.5 use bisection method to three iterations by hand.
Use bisection to determine the drag coefficient needed so that an 80-kg parachutist has a velocity of 36 m/s after 4 s of free fall. Note: The acceleration of gravity is 9.81 m/s2 . Start with initial guesses of xl = 0.1 and xu = 0.2 and iterate until the approximate relative error falls below 2%.
3. Using the trial function u¹(x) = a sin(x) and weighting function w¹(x) = b sin(x) find an approximate solution to the following boundary value problems by determining the value of coefficient a. For each one, also find the exact solution using Matlab and plot the exact and approximate solutions. (One point each for: (i) finding a, (ii) finding the exact solution, and (iii) plotting the solution) a. (U₁xx -2 = 0 u(0) = 0 u(1) = 0 b. Modify the trial function and find an approximation for the following boundary value problem. (Hint: you will need to add an extra term to the function to make it satisfy the boundary conditions.) (U₁xx-2 = 0 u(0) = 1 u(1) = 0
3. Using the trial function uh(x) = a sin(x) and weighting function wh(x) = b sin(x) find an approximate solution to the following boundary value problems by determining the value of coefficient a. For each one, also find the exact solution using Matlab and plot the exact and approximate solutions. (One point each for: (i) finding a, (ii) finding the exact solution, and (iii) plotting the solution) a. (U₁xx - 2 = 0 u(0) = 0 u(1) = 0 b. Modify the trial function and find an approximation for the following boundary value problem. (Hint: you will need to add an extra term to the function to make it satisfy the boundary conditions.) (U₁xx - 2 = 0 u(0) = 1 u(1) = 0
Consider the function p(x) = x² - 4x³+3x²+x-1. Use Newton-Raphson's method with initial guess of 3. What's the updated value of the root at the end of the second iteration? Type your answer...
(3) Method. Print the code and the answer for an error tolerance &₁ = 0.01%. Problem 5.14: Hint: you can reuse code from above. Print the Matlab code, and clearly indicate your answer.
Please help, this for Matlab the image is the first question with following 2 and 3 they go together. 2. Solving the question by using bisection.m with the stopping criterion at 1%. Report the root and # of iterations. 3. by using newton-Raphson matlab script with the stopping criterion at 0.1%. Report the root and # of iterations.
Q-2) Find the solution for the LPP below by using the graphical method? Min Z=4x1+3x2 S.to: x1+2x2<6 2x1+x2<8 x127 x1,x2 ≥ 0 Is there an optimal solution and why if not can you extract it?
The natural exponential function can be expressed by . Determine e2by calculating the sum of the series for:(a) n = 5, (b) n = 15, (c) n = 25For each part create a vector n in which the first element is 0, the incrementis 1, and the last term is 5, 15, or 25. Then use element-by-element calculations to create a vector in which the elements are . Finally, use the MATLAB built-in function sum to add the terms of the series. Compare thevalues obtained in parts (a), (b), and (c) with the value of e2calculated byMATLAB.
For the DE: dy/dx=2x-y y(0)=2 with h=0.2, solve for y using each method below in the range of 0 <= x <= 3: Q1) Using Matlab to employ the Euler Method (Sect 2.4) Q2) Using Matlab to employ the Improved Euler Method (Sect 2.5 close all clear all % Let's program exact soln for i=1:5 x_exact(i)=0.5*i-0.5; y_exact(i)=-x_exact(i)-1+exp(x_exact(i)); end plot(x_exact,y_exact,'b') % now for Euler's h=0.5 x_EM(1)=0; y_EM(1)=0; for i=2:5 x_EM(i)=x_EM(i-1)+h; y_EM(i)=y_EM(i-1)+(h*(x_EM(i-1)+y_EM(i-1))); end hold on plot (x_EM,y_EM,'r') % Improved Euler's Method h=0.5 x_IE(1)=0; y_IE(1)=0; for i=2:1:5 kA=x_IE(i-1)+y_IE(i-1); u=y_IE(i-1)+h*kA; x_IE(i)=x_IE(i-1)+h; kB=x_IE(i)+u; k=(kA+kB)/2; y_IE(i)=y_IE(i-1)+h*k; end hold on plot(x_IE,y_IE,'k')

SEE MORE QUESTIONS

Recommended textbooks for you

Principles of Heat Transfer (Activate Learning wi…

Mechanical Engineering

ISBN:

9781305387102

Author:

Kreith, Frank; Manglik, Raj M.

Publisher:

Cengage Learning