11.1.4 - Algorithm: Step-by-Step Implementation
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Practice Questions
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Define Heun's Method.
💡 Hint: Think about its relationship to Euler's Method.
What is the first step when using Heun's Method?
💡 Hint: What do you set before starting the calculations?
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does Heun's Method primarily improve upon compared to Euler's Method?
💡 Hint: Think about what aspect of numerical methods is being enhanced.
Heun's Method utilizes what type of approach?
💡 Hint: Consider the steps involved in this method.
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Challenge Problems
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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.
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.
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