Practice Example Problem (11.1.5) - Heun’s Method - Mathematics - iii (Differential Calculus)

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6 sample questions

Question 1.
What is the primary purpose of Heun's Method?
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Think about the equations used in modeling scientific problems.
Question 2.
What formula do you use for the predictor step in Heun’s Method?
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Recall the notation used in the section.
3Question 3.
What order of accuracy does Heun's Method possess?
- First
- Second
- Third
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Recall the comparison made against Euler's Method in class.
4Question 4.
True or False: Heun’s Method requires only one function evaluation per step.
- True
- False
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Consider the steps involved in the method.
Question 5.
Using Heun’s Method, find the approximation of y at x = 0.2 for the function dy/dx = y - x with y(0) = 0.3. Show all steps and calculations.
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Pay close attention to each slope calculation.
Question 6.
Discuss why Heun’s Method might not perform well on stiff equations, providing a specific example.
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Consider the nature of the differential equation and impacts on numerical stability.

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