Practice Numerical Method (18.1.2) - Stability and Convergence of Methods

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6 sample questions

Question 1.
Define a numerical method.
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Think about how we can calculate using previous values.
Question 2.
What does the step size $h$ indicate?
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A smaller step size generally leads to more accuracy.
3Question 3.
What is a numerical method?
- A way of exact solutions
- An approximation procedure
- Only for linear equations
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Think about how we address complex ODEs.
4Question 4.
True or False: A smaller step size results in larger local truncation error.
- True
- False
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Recall the relationship between step size and accuracy.
Question 5.
Formulate a numerical method to solve the ODE $y' = -3y$ with the initial condition $y(0) = 2$ using h = 0.5.
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Pay attention to the signs while calculating the next values.
Question 6.
Analyze the stability of the numerical method applied to the equation $y' = -y$ . What does your analysis suggest about step size?
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Consider the implications for large values of h.

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