11.1.1. Introduction

Try these first

1. 1.

   What does Heun's Method improve upon compared to Euler's Method?

   Hint

   Think about the slopes used in both methods.

2. 2.

   Define an Initial Value Problem (IVP).

   Hint

   Consider where we start solving the equation.

3. 3.

   What is Heun’s Method primarily used for?

   • Exact solutions of ODEs
   • Numerical approximation of ODEs
   • Graphing ODEs

   Hint

   Consider what happens when exact solutions are unavailable.

4. 4.

   True or False: Heun's Method is less accurate than Euler's Method.

   • True
   • False

   Hint

   Recall the method's definition.

5. 5.

   You have an ODE: dy/dx = -2y with y(0) = 1. Use Heun’s Method with a step size of 0.05 to find y(0.1). Show all steps.

   Hint

   Keep track of your calculations at each step.

6. 6.

   Explain how you would implement Heun’s Method in a programming language like Python and describe potential pitfalls.

   Hint

   Consider the iterative process and how it affects result accuracy.