Given this boundary-value problem: d²y y + d0² 4 which has the solution y = 2 sin(0/2), 0, y(0) = 0, y(t) = 2,

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60. Given this boundary-value problem:
d'y y
+
d0² 4
=
0, y(0) = 0, y(t) = 2,
which has the solution
a. Solve, using finite difference approximations to the
derivative with h = 7/4 and tabulate the errors.
b. Solve again by finite differences but with a value of h
small enough to reduce the maximum error to 0.5%.
Can you predict from part (a) how small h should be?
c. Solve again by the shooting method. Find how large
h can be to have maximum error of 0.5%.
y 2 sin(0/2),
=
Transcribed Image Text:60. Given this boundary-value problem: d'y y + d0² 4 = 0, y(0) = 0, y(t) = 2, which has the solution a. Solve, using finite difference approximations to the derivative with h = 7/4 and tabulate the errors. b. Solve again by finite differences but with a value of h small enough to reduce the maximum error to 0.5%. Can you predict from part (a) how small h should be? c. Solve again by the shooting method. Find how large h can be to have maximum error of 0.5%. y 2 sin(0/2), =
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