Practice Summary (11.1.11) - Heun’s Method - Mathematics - iii (Differential Calculus)

Practise this section

9 questions

Flashcard drill
3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
3 questions · about 2 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
Explain the purpose of Heun's Method.
Show hintHide hint
Think about the challenges of solving ODEs directly.
Question 2.
What initial condition is given in our example problem?
Show hintHide hint
Recall what the initial value represents in an IVP.
3Question 3.
What is the main advantage of Heun’s Method over Euler’s Method?
- Lower accuracy
- Higher accuracy
- More complex calculations
Show hintHide hint
Consider the benefits of calculating two slopes.
4Question 4.
Is Heun's Method more stable than Euler's Method?
- True
- False
Show hintHide hint
Recall the properties of both methods.
Question 5.
Using Heun's Method, determine $y(0.2)$ for the equation $rac{dy}{dx} = 2y$ with an initial condition of $y(0) = 1$ and step size of 0.1. Show all steps.
Show hintHide hint
Make sure to clearly show each stage of your calculations.
Question 6.
Explain why Heun’s Method is classified as a second-order method and compare it to a first-order method. Provide examples.
Show hintHide hint
Reference the definitions of order and error for both methods.

5 more questions in this section. Enroll free to practise them all.