Exercise 3.2.4 (Compare the results here to Exercise 3.1.5.) Apply the improved Euler's method to the ODE u' (t) = u² (t) with u(0) = 1 to estimate u(2) using step sizes h = 1,0.1,0.01, and 0.001. Explain what's going on. Hint: compute the analytical solution using separation of variables. Then recall Definition 2.4.1 and the notion of the maximum domain of a solution from Section 2.4.2.
Exercise 3.2.4 (Compare the results here to Exercise 3.1.5.) Apply the improved Euler's method to the ODE u' (t) = u² (t) with u(0) = 1 to estimate u(2) using step sizes h = 1,0.1,0.01, and 0.001. Explain what's going on. Hint: compute the analytical solution using separation of variables. Then recall Definition 2.4.1 and the notion of the maximum domain of a solution from Section 2.4.2.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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3.2.4
Transcribed Image Text:DEC
Exercise 3.2.3 Apply the improved Euler's method to the ODE u' (t) = u(t)-t+1 with
u(0) = 0, to estimate u(1) using step sizes h= 1,0.1, and 0.01. Then find the analytical solution
and compute the error for each step size. Why does this make perfect sense?
u(4) using step sizes h = = 1.0, 0.1,0.01.
Exercise 3.2.4 (Compare the results here to Exercise 3.1.5.) Apply the improved Euler's
method to the ODE u' (t) = u²(t) with u(0) = 1 to estimate u(2) using step sizes h = 1,0.1,0.01,
and 0.001. Explain what's going on. Hint: compute the analytical solution using separation of
variables. Then recall Definition 2.4.1 and the notion of the maximum domain of a solution
from Section 2.4.2.
Exercise 3.2.5 (Compare the results here to Exercise 3.1.6.) Consider the linear ODE
u' (t) = u(t)- sin(t) + cos(t).
tv
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