18 - Numerical Solutions of ODEs
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Practice Questions
Test your understanding with targeted questions
Define an Ordinary Differential Equation (ODE).
💡 Hint: Think about what you aim to find.
What is a numerical method?
💡 Hint: Consider the context of computations.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the definition of stability in numerical methods?
💡 Hint: Think about error behavior.
True or False: For convergence to occur, stability must also be present.
💡 Hint: Recall the relationship between consistency and stability.
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Challenge Problems
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Using the differential equation y' = -2y, apply Euler's method with h = 0.5 starting at y(0) = 1. Discuss the stability and how errors might evolve.
💡 Hint: Consider the implications of stability on your results.
Prove the relationship between consistency, stability, and convergence using an example of your choice.
💡 Hint: Work through a specific example methodically.
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