Practice Fundamental Concepts (18.1) - Stability and Convergence of Methods

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6 sample questions

Question 1.
Define an Ordinary Differential Equation.
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Focus on the function and derivatives.
Question 2.
What is a numerical method?
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Think about how we use methods to calculate values.
3Question 3.
What is the definition of an Ordinary Differential Equation (ODE)?
- A type of algebraic equation
- An equation involving functions and their derivatives
- A polynomial equation
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Think about the components of an ODE.
4Question 4.
True or False: Stability ensures that errors grow uncontrollably.
- True
- False
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Remember the definition of stability.
Question 5.
Given the ODE y' = -3y with initial condition y(0) = 2, apply Euler’s method with a step size of 0.5 to find the approximation at x = 1.
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Pay attention to how you apply the recurrence relation.
Question 6.
Analyze the convergence of the numerical solution for the ODE y' = -y as h approaches zero, discussing the impact on accuracy.
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Consider what happens as you make step sizes smaller.

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