Solve the following initial-value problem over the interval from t = 2 to t = 3: dy/dt = –0.4y + e-2t Use the non-self-starting Heun method with a step size of 0.5 and initial conditions of y(1.5) =...

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Solve the following initial-value problem over the interval from t = 2 to t = 3:
dy/dt = –0.4y + e-2t
Use the non-self-starting Heun method with a step size of 0.5 and initial conditions of y(1.5) = 5.800007 and y(2.0) = 4.762673. Iterate the corrector to es = 0.1%. Compute the true percent relative errors et for your results based on the analytical solution.




Answered Same DayDec 24, 2021

Answer To: Solve the following initial-value problem over the interval from t = 2 to t = 3: dy/dt = –0.4y +...

David answered on Dec 24 2021
127 Votes
The analytical solution is

tt eey 24.0 625.0625.10  
Therefore, the exact results are y(2.
5) = 3.904508 and y(3) = 3.198639.
First step:
Predictor:
y1
0
= 5.800007+[0.4(4.762673)+e
2(2)
]1 = 3.913253
Corrector:...
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