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Solving an IVP with Maple : Euler and Improved Euler Method

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Use Maple to solve this exercise:
Consider the following (IVP) logistic model
p' = 10p(1-p) with p(0)=0.1

1. Solve this IVP and graph the solution over the interval [0, 10], Write down the Euler approximation, and Improved Euler approximation with step size h.

2. Compute and plot the first 100 points of the Euler method for h=0.1, 0.18, 0.23, 0.25, 0.26, 0.28, and 0.3. Discuss your findings.

3. Beginning at h=0.18, compute the values of the first 200 Euler approximations and record the next 30 values. Increase h by 0.001 and repeat this process until h=0.30. Plot the diagram and compare with #2.

4. Redo #3 but use the Improved Euler method instead. Discuss your findings.

5. Redo #4 until h=0.40. Discuss your findings.

Please see the attached file for the fully formatted problems.

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An IVP is solved with Maple using Euler and Improved Euler Methods. The solution is detailed and well presented.

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