Practice Stability (18.2.2) - Stability and Convergence of Methods - Mathematics - iii (Differential Calculus) - Vol 4

Practice: Stability

Lesson 18.2.2Stability and Convergence of Methods

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8 questions

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6 sample questions

Question 1.
What is stability in numerical methods?
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Think about how errors affect the numerical solution.
Question 2.
Define absolute stability.
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Consider the meaning of a bounded growth of errors.
3Question 3.
What determines the stability of a numerical method?
- A) The method's accuracy
- B) The behavior of errors under perturbations
- C) The initial conditions
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Think about what happens when perturbations occur.
4Question 4.
True or False: A stable method will always provide the correct solution.
- True
- False
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Remember the relation between stability and convergence.
Question 5.
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.
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Calculate the stability function and check the modulus.
Question 6.
Given a multistep method, analyze its stability region and identify if it would be suitable for stiff ODEs. Explain your reasoning.
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Determine the relationship between roots of the characteristic equation and the unit circle.

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