EBK NUMERICAL METHODS FOR ENGINEERS
7th Edition
ISBN: 9780100254145
Author: Chapra
Publisher: YUZU
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Textbook Question
Chapter 22, Problem 13P
Develop a user-friendly computer program for Gauss quadrature. Test it by duplicating the results of Examples 22.3 and 22.4 and the function in Prob. 22.10.
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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?
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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
Chapter 22 Solutions
EBK NUMERICAL METHODS FOR ENGINEERS
Ch. 22 - 22.1 Use order of Romberg integration to...Ch. 22 - Use Romberg integration to evaluate I=12(x+1x)2dx...Ch. 22 - Use Romberg integration to evaluate 02exsinx1+x2dx...Ch. 22 - Obtain an estimate of the integral from Prob....Ch. 22 - Obtain an estimate of the integral from Prob....Ch. 22 - 22.6 Obtain an estimate of the integral from Prob....Ch. 22 - 22.7 Perform the computation in Examples 21.3 and...Ch. 22 - Employ two- through six-point Gauss-Legendre...Ch. 22 - Prob. 9PCh. 22 - 22.10 Develop a user-friendly computer program for...
Ch. 22 - Develop a user-friendly computer program for...Ch. 22 - Develop a user-friendly computer program for...Ch. 22 - 22.13 Develop a user-friendly computer program for...Ch. 22 - There is no closed form solution for the error...Ch. 22 - 22.15 The amount of mass transported via a pipe...Ch. 22 - The depths of a river H are measured at equally...Ch. 22 - 22.17 Recall that the velocity of the freefalling...Ch. 22 - 22.18 Prove that Eq. (22.15) is equivalent to...
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