11.1.7 - Comparison with Euler’s Method
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Practice Questions
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What is the primary advantage of Heun’s method over Euler’s method?
💡 Hint: Think about the number of slopes used in both methods.
How many function evaluations are required for one step in Heun’s method?
💡 Hint: Consider the predictor and corrector steps.
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Interactive Quizzes
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Which of the following best describes Heun's method?
💡 Hint: Recall the definitions of different order methods.
True or False: Heun's method requires only one evaluation of the function per step.
💡 Hint: Think about the predictor and corrector steps in Heun's method.
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Challenge Problems
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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.
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).
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