Euler’s Method Let’s get our hands dirty and actually useEuler’s method to estimate the value of y(2) where y is thesolution to the initial value problem
y?=y?2x y(0)= 1
Recall that Euler’s method says: Approximate values for thesolution of the initial value problem
y?=F(x, y),y(x0) =y0 with step size h, at xn=xn?1+h, are
yn=yn?1+hF(xn?1, yn?1)
Fill in the table for steps of size h= 0.2.
| n | xn | yn=yn-1+0.2F(xn-1,Yn-1 | y'=F(xn,yn) |
| 0 | 0 | 1 | |
| 1 | .2 | | |
| 2 | .4 | | |
| 3 | | | |
| 4 | | | |
| 5 | | | |
| 6 | | | |
| 7 | | | |
| 8 | | | |
| 9 | | | |
| 10 | | | |
Graph the portion of the approximate solution curve you foundabove. It should look like a lot of line segments. The firstsegment has been given on the grid below:
(c) Suppose f(x) is an exact solution to the initial valueproblem above. Describe, with justification, the behavior off(x) asx??. Hint: Graphing a slope field may be helpful for this.
