11. Numerical Solutions of ODEs I

Euler’s Method — Quiz

Test your understanding of euler’s method with 5 practice questions.

Practice Questions

Question 1

What is the main idea of Euler's method for approximating the solution of an initial value problem?

Question 2

For an initial value problem $y'=f(x,y)$, which formula gives one Euler step from $\left(x_n,y_n\right)$?

Question 3

Use one step of Euler's method for $y'=x+y$ with $y(0)=1$ and step size $h=0.1$. What is the value of $y_1$?

Question 4

Use one step of Euler's method for $y'=2y$ with $y(0)=3$ and step size $h=0.2$. What is $y_1$?

Question 5

What usually happens to the accuracy of Euler's method when the step size $h$ is made smaller?