Considering Y' (t) = Y()+²-2, Y(0) = 2. Given the true solution is Y(t) = t² + 2t + 2-2(t+1) log(t+1). a) Use Euler method compute Y(t) for h=0.5, to estimate the value when t = 1,t=2,t = 3,t = 4 and t = 5. Compute the true error. Show the results in a table. b) Next, use step size h=0.2, for the same range. Compute the true error. Conclude the findings from the error.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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QUESTION 2
Considering Y' (t) = Y()+t²-2, Y(0) = 2.
Given the true solution is Y(t) = t² + 2t + 2-2(t+1) log(t + 1).
a)
b)
Use Euler method compute Y(t) for h-0.5, to estimate the value when
t = 1,t = 2, t = 3,t = 4 and t = 5. Compute the true error. Show the
results in a table.
Next, use step size h=0.2, for the same range. Compute the true error.
Conclude the findings from the error.
Transcribed Image Text:QUESTION 2 Considering Y' (t) = Y()+t²-2, Y(0) = 2. Given the true solution is Y(t) = t² + 2t + 2-2(t+1) log(t + 1). a) b) Use Euler method compute Y(t) for h-0.5, to estimate the value when t = 1,t = 2, t = 3,t = 4 and t = 5. Compute the true error. Show the results in a table. Next, use step size h=0.2, for the same range. Compute the true error. Conclude the findings from the error.
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