18.2.1 - Consistency
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Practice Questions
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What is the local truncation error?
💡 Hint: Think about what happens in a single step of approximation.
How does the step size ℎ affect consistency?
💡 Hint: Consider what happens as we make steps smaller.
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Interactive Quizzes
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What does consistency in numerical methods refer to?
💡 Hint: Think about how error behaves as we reduce our step size.
True or False: A method can be consistent and not convergent.
💡 Hint: Reflect on the relationship between consistency and other properties.
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Challenge Problems
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Given the function y' = -y, apply Euler's method with various step sizes (0.1, 0.01, 0.001) to compute the local truncation error at each step. Analyze how the error decreases.
💡 Hint: Calculate at each step and compare the approximations to the actual solution.
Devise a new numerical method and analyze its consistency and stability. Carry out a detailed error analysis comparing it to Euler's method.
💡 Hint: Consider different functions and step sizes in your evaluations.
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