Numerical Analysis
Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Chapter 7.2, Problem 1CP

Use finite differences to approximate solutions to the linear BVPs for n = 9 , 19 , and 39 .

a. { y = y + 2 3 e t y ( 0 ) = 0 y ( 1 ) = 1 3 e

b. { y = ( 2 + 4 t 2 ) y y ( 0 ) = 1 y ( 1 ) = e

Plot the approximate solutions together with the exact solutions (a) y ( t ) = t e t / 3 and (b) y ( t ) = e t 2 , and display the errors as a function of t in a separate semilog plot.

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