11.1.11. Summary

Try these first

1. 1.

   Explain the purpose of Heun's Method.

   Hint

   Think about the challenges of solving ODEs directly.

2. 2.

   What initial condition is given in our example problem?

   Hint

   Recall what the initial value represents in an IVP.

3. 3.

   What is the main advantage of Heun’s Method over Euler’s Method?

   • Lower accuracy
   • Higher accuracy
   • More complex calculations

   Hint

   Consider the benefits of calculating two slopes.

4. 4.

   Is Heun's Method more stable than Euler's Method?

   • True
   • False

   Hint

   Recall the properties of both methods.

5. 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.

   Hint

   Make sure to clearly show each stage of your calculations.

6. 6.

   Explain why Heun’s Method is classified as a second-order method and compare it to a first-order method. Provide examples.

   Hint

   Reference the definitions of order and error for both methods.