11.1.4. Algorithm: Step-by-Step Implementation

Try these first

1. 1.

   Define Heun's Method.

   Hint

   Think about its relationship to Euler's Method.

2. 2.

   What is the first step when using Heun's Method?

   Hint

   What do you set before starting the calculations?

3. 3.

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

   • Accuracy
   • Speed
   • Complexity

   Hint

   Think about what aspect of numerical methods is being enhanced.

4. 4.

   Heun's Method utilizes what type of approach?

   • Predictor-Corrector
   • Single-Step
   • Multi-Step

   Hint

   Consider the steps involved in this method.

5. 5.

   Solve the differential equation dy/dx = -2y + 2, with y(0) = 1 using Heun's Method for the interval [0, 0.5] with h = 0.1. Compare your results to the analytical solution.

   Hint

   Follow the predictor and corrector steps closely.

6. 6.

   For the equation dy/dx = y^2 - x^2, where y(0) = 0, apply Heun’s Method over the range [0, 0.1] and explain the impact of step size on accuracy.

   Hint

   Consider how smaller h values can yield closer results to the true function.