11. Numerical Solutions of ODEs I

Stability Considerations — Quiz

Test your understanding of stability considerations with 5 practice questions.

Practice Questions

Question 1

In numerical ODEs, what does stability most nearly mean?

Question 2

For the test equation $y'=\lambda y$ with $\lambda=-2$, explicit Euler gives $y_{n+1}=(1-2h)y_n$. For stability, what condition on $h$ is required?

Question 3

If the amplification factor of a numerical method has magnitude greater than $1$, what typically happens to errors?

Question 4

Which method is generally more stable for stiff problems?

Question 5

For explicit Euler, what is one common effect of decreasing the step size $h$ on stability?