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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is stability in numerical methods?
💡 Hint: Think about how errors affect the numerical solution.
Question 2
Easy
Define absolute stability.
💡 Hint: Consider the meaning of a bounded growth of errors.
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 determines the stability of a numerical method?
- A) The method's accuracy
- B) The behavior of errors under perturbations
- C) The initial conditions
💡 Hint: Think about what happens when perturbations occur.
Question 2
True or False: A stable method will always provide the correct solution.
- True
- False
💡 Hint: Remember the relation between stability and convergence.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Consider the differential equation \( y' = -2y \) solved by Euler's method. If you choose a step size of \( h = 0.5 \), is this method stable? Justify your answer using the stability function.
💡 Hint: Calculate the stability function and check the modulus.
Question 2
Given a multistep method, analyze its stability region and identify if it would be suitable for stiff ODEs. Explain your reasoning.
💡 Hint: Determine the relationship between roots of the characteristic equation and the unit circle.
Challenge and get performance evaluation