11.1.7. Comparison with Euler’s Method

Try these first

1. 1.

   What is the primary advantage of Heun’s method over Euler’s method?

   Hint

   Think about the number of slopes used in both methods.

2. 2.

   How many function evaluations are required for one step in Heun’s method?

   Hint

   Consider the predictor and corrector steps.

3. 3.

   Which of the following best describes Heun's method?

   • A first-order method
   • A second-order method
   • A third-order method

   Hint

   Recall the definitions of different order methods.

4. 4.

   True or False: Heun's method requires only one evaluation of the function per step.

   • True
   • False

   Hint

   Think about the predictor and corrector steps in Heun's method.

5. 5.

   Using the ODE dy/dx = y^2 - x at y(0) = 0, apply Heun's method with h = 0.1 to approximate y(0.2).

   Hint

   Repeat the steps twice in the same way as described in the section.

6. 6.

   When given an initial value problem y' = e^(-t) - y with an initial condition y(0) = 1, use Heun’s method, h = 0.5, to approximate y at t = 0.5.

   Hint

   Remember to calculate e^(-t).