Practice Worked Example (16.6) - Error Analysis in Numerical ODE Solutions

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6 sample questions

Question 1.
What equation do we need to solve in the worked example?
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Look for the function you’ll use in your calculation.
Question 2.
What was the initial condition given in the example?
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Check the values of y at the start of the problem.
3Question 3.
What is the main advantage of the Adams-Moulton method?
- Less accurate
- Higher accuracy
- Simpler to compute
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Remember its application in solving stiff ODEs.
4Question 4.
True or False: The Adams-Moulton method requires solving equations at each step.
- True
- False
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Think about how we derive the next point.
Question 5.
Solve the ODE dy/dx = 3x^2 + 2y with y(0) = 1 using a 2-step Adams-Moulton method with h = 0.1.
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You will need to compute f at various steps before applying the rule.
Question 6.
Given the function f(x, y) = x*y + x^2, use the Adams-Moulton method to estimate y(0.1) if y(0) = 2 with h = 0.1.
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Identify f_0 and f_1 before applying the formula.

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