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

Question

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) = XXXXXXXXXXand y(2.0) = XXXXXXXXXXIterate the corrector to es = 0.1%. Compute the true percent relative errors et for your results based on the analytical solution.

David · Accepted Answer

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: 
901344.35.0
2
)913253.3(4.0)762673.4(4.0
762673.4
)5.

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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