Numerical Analysis
Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Chapter 7.3, Problem 2CP

Use the Collocation Method with n = 8 , 16 to approximate solutions to the linear boundary value problems

a. { 9 y + π 2 y = 0 y ( 0 ) = 1 y ( 3 2 ) = 3

b. { y = 3 y 2 y y ( 0 ) = e 3 y ( 1 ) = 1

Plot the approximate solutions together with the exact solutions (a)

y ( t ) = 3 sin π t / 3 cos π t / 3 and (b)

y ( t ) = e 3 3 t , and display the errors as a function of t in a separate semilog plot.

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