Practice Introduction (11.1.1) - Heun’s Method - Mathematics - iii (Differential Calculus)

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6 sample questions

Question 1.
What does Heun's Method improve upon compared to Euler's Method?
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Think about the slopes used in both methods.
Question 2.
Define an Initial Value Problem (IVP).
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Consider where we start solving the equation.
3Question 3.
What is Heun’s Method primarily used for?
- Exact solutions of ODEs
- Numerical approximation of ODEs
- Graphing ODEs
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Consider what happens when exact solutions are unavailable.
4Question 4.
True or False: Heun's Method is less accurate than Euler's Method.
- True
- False
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Recall the method's definition.
Question 5.
You have an ODE: dy/dx = -2y with y(0) = 1. Use Heun’s Method with a step size of 0.05 to find y(0.1). Show all steps.
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Keep track of your calculations at each step.
Question 6.
Explain how you would implement Heun’s Method in a programming language like Python and describe potential pitfalls.
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Consider the iterative process and how it affects result accuracy.

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