11.1.5. Example Problem

Try these first

1. 1.

   What is the primary purpose of Heun's Method?

   Hint

   Think about the equations used in modeling scientific problems.

2. 2.

   What formula do you use for the predictor step in Heun’s Method?

   Hint

   Recall the notation used in the section.

3. 3.

   What order of accuracy does Heun's Method possess?

   • First
   • Second
   • Third

   Hint

   Recall the comparison made against Euler's Method in class.

4. 4.

   True or False: Heun’s Method requires only one function evaluation per step.

   • True
   • False

   Hint

   Consider the steps involved in the method.

5. 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.

   Hint

   Pay close attention to each slope calculation.

6. 6.

   Discuss why Heun’s Method might not perform well on stiff equations, providing a specific example.

   Hint

   Consider the nature of the differential equation and impacts on numerical stability.