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2 cards from this section. Quick, good the night before a test.
What is the local truncation error?
Think about what happens in a single step of approximation.
How does the step size ℎ affect consistency?
Consider what happens as we make steps smaller.
What does consistency in numerical methods refer to?
Think about how error behaves as we reduce our step size.
True or False: A method can be consistent and not convergent.
Reflect on the relationship between consistency and other properties.
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.
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.
Consider different functions and step sizes in your evaluations.
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