Numerical Analysis
Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Chapter 7.2, Problem 7CP

Extrapolate the approximate solutions in Computer Problem 5. Apply Richardson extrapolation (Section 5.1) to the formula

N ( h ) = w h ( 1 / 2 ) , the finite difference approximation with step size h . How close can extrapolation get to the exact value

y ( 1 / 2 ) by using only the approximate values from

h = 1 / 4 , 1 / 8 , and

1 / 16

?

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Chapter 7 Solutions

Numerical Analysis

Ch. 7.1 - Use Theorem 7.1 to prove that the boundary value...Ch. 7.1 - Show that the solutions to the BVPs in Exercise 1...Ch. 7.1 - Consider the BVP { y=cyy(a)=yay(b)=yb where c0, ab...Ch. 7.1 - Consider the BVP { y=cyy(0)=0y(b)=0 where c0. For...Ch. 7.1 - Prob. 5ECh. 7.1 - Prob. 6ECh. 7.1 - Show that the solutions to the linear BVPs {...Ch. 7.1 - Prob. 8ECh. 7.1 - Prob. 9ECh. 7.1 - Apply the Shooting Method to the linear BVPs....
Ch. 7.1 - Carry out the steps of Computer Problem 1 for the...Ch. 7.1 - Apply the Shooting Method to the nonlinear BVPs....Ch. 7.1 - Carry out the steps of Computer Problem 3 for the...Ch. 7.1 - Prob. 5CPCh. 7.1 - Verify that (7.10) is a solution of the BVP for...Ch. 7.1 - Set compressibility to the moderate value c=0.01 ....Ch. 7.1 - Prob. 3SACh. 7.1 - Change pressure to p=3.5, and resolve the BVP....Ch. 7.1 - Prob. 5SACh. 7.1 - Carry out Step 5 for the reduced compressibility...Ch. 7.1 - Carry out Step 5 for increased compressibility...Ch. 7.2 - Use finite differences to approximate solutions to...Ch. 7.2 - Use finite differences to approximate solutions to...Ch. 7.2 - Use finite differences to approximate solutions to...Ch. 7.2 - Use finite differences to plot solutions to the...Ch. 7.2 - (a) Find the solution of the BVP y=y, y(0)=0,...Ch. 7.2 - Solve the nonlinear BVP 4y=ty4, y(1)=2, y(2)=1 by...Ch. 7.2 - Extrapolate the approximate solutions in Computer...Ch. 7.2 - Extrapolate the approximate solutions in Computer...Ch. 7.2 - Prob. 9CPCh. 7.2 - Use finite differences to solve the equation {...Ch. 7.2 - Solve { y=cy(1y)y(0)=0y(1/2)=1/4y(1)=1 for c0,...Ch. 7.3 - Use the Collocation Method with n=8, 16 to...Ch. 7.3 - Use the Collocation Method with n=8, 16 to...Ch. 7.3 - Carry out the steps of Computer Problem 1, using...Ch. 7.3 - Carry out the steps of Computer Problem 2, using...
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