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2 cards from this section. Quick, good the night before a test.
Define Heun's Method.
Think about its relationship to Euler's Method.
What is the first step when using Heun's Method?
What do you set before starting the calculations?
What does Heun's Method primarily improve upon compared to Euler's Method?
Think about what aspect of numerical methods is being enhanced.
Heun's Method utilizes what type of approach?
Consider the steps involved in this method.
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.
Follow the predictor and corrector steps closely.
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.
Consider how smaller h values can yield closer results to the true function.
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