11.1. Heun’s Method

Try these first

1. 1.

   Explain the difference between predictor and corrector in Heun's Method.

   Hint

   Think about how each step contributes to finding the next value.

2. 2.

   What type of problems is Heun's Method used for?

   Hint

   What do we mean by initial value?

3. 3.

   What is Heun’s Method used for?

   • Numerical differentiation
   • Solving ODEs
   • Graph plotting

   Hint

   Think of how it relates to differential equations.

4. 4.

   True or False: Heun’s Method is more accurate than Euler’s Method.

   • True
   • False

   Hint

   Recall how each method handles slope calculations.

5. 5.

   Given the differential equation dy/dx = -y^2 + 2, with y(0) = 1, find y(0.1) using Heun's Method and step size h = 0.1. Analyze if the answer is reasonable or not.

   Hint

   Check your calculations at each predictor and corrector step.

6. 6.

   For the equation dy/dx = x - y, y(0) = 0.5, estimate y(0.2) using Heun's Method with h = 0.1. Discuss the significance of your result.

   Hint

   Investigate if this aligns with a physical interpretation in terms of growth or decay.