12. Numerical Solutions of ODEs II

System Approximations — Quiz

Test your understanding of system approximations with 5 practice questions.

Practice Questions

Question 1

If $y_1=y$ and $y_2=y'$, which system is equivalent to $y''+y=0$?

Question 2

What is the main reason to convert a higher-order ODE to a first-order system in system approximations?

Question 3

If $y(0)=2$ and $y'(0)=-1$, and $y_1=y$, $y_2=y'$, what is the initial vector $Y(0)$?

Question 4

Rewrite $y''=3y'+2y$ as a first-order system using $y_1=y$ and $y_2=y'$.

Question 5

In a system approximation, the unknown solution at one step is usually represented as