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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the local truncation error?
💡 Hint: Think about what happens in a single step of approximation.
Question 2
Easy
How does the step size ℎ affect consistency?
💡 Hint: Consider what happens as we make steps smaller.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What does consistency in numerical methods refer to?
- Local truncation error approaches zero as step size decreases
- Numerical solutions being exact
- Stability of numerical methods
💡 Hint: Think about how error behaves as we reduce our step size.
Question 2
True or False: A method can be consistent and not convergent.
- True
- False
💡 Hint: Reflect on the relationship between consistency and other properties.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
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.
Question 2
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.
Challenge and get performance evaluation