18.2.2 - Stability
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Practice Questions
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What is stability in numerical methods?
💡 Hint: Think about how errors affect the numerical solution.
Define absolute stability.
💡 Hint: Consider the meaning of a bounded growth of errors.
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Interactive Quizzes
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What determines the stability of a numerical method?
💡 Hint: Think about what happens when perturbations occur.
True or False: A stable method will always provide the correct solution.
💡 Hint: Remember the relation between stability and convergence.
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Challenge Problems
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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.
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.
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