18.2 - Consistency, Stability, and Convergence
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Practice Questions
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Define consistency in the context of numerical methods.
💡 Hint: Think about how the accuracy of numerical methods improves with smaller steps.
What does a stable numerical method imply?
💡 Hint: Consider what we do with rounding errors.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the definition of consistency in numerical methods?
💡 Hint: Look for the relationship between step size and accuracy.
Is a stable method guaranteed to converge?
💡 Hint: Recall the Lax Equivalence Theorem.
2 more questions available
Challenge Problems
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Consider a numerical method that has a consistent local truncation error but demonstrates growing errors due to rounding each step. Discuss the potential challenges faced in applying this method.
💡 Hint: Focus on the implications of error growth in larger calculations.
Demonstrate the implications of the Lax Equivalence Theorem in practical numerical methods by providing an example of a method that fails to converge due to lack of stability.
💡 Hint: Reflect on common methods in numerical algorithms and identify characteristics.
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