Questions

01

Euler’s method practice

Consider the IVP:

$$y^{\prime }=2y-3t,y(0)=1.$$

Use Euler’s method to compute an approximate solution up to $t=0.20$ with step size $h=0.05$. Show all four steps of the partial solution.

02

Heun’s method practice

Consider the IVP:

$$y^{\prime }=2y-3t,y(0)=1.$$

Use Heun’s method to compute an approximate solution up to $t=0.20$ with step size $h=0.05$. Show all four steps of the partial solution.

03

Comparing methods

Solve algebraically the IVP as in the previous Questions: $y^{\prime }=2y-3t,y(0)=1$. Make a table of values to compare the results of Euler’s method, Heun’s method, and the exact solution. Write the percent error next to the values from the approximation methods. Create a final column that includes the percent difference between the approximate solutions. Can this column predict the percent error without knowing the exact solution?