# Calibrating the Euler Method

$f(x)=-x$ and initial condition $x(0)=1$

Using the Euler Method with the step size $\Delta t=1$, estimate $x(1)$ numerically.

I so far did:

$X_{n+1} = X_n+f(x_n)(1)$

$X_1=0$

$X_2=0$

I have a similar question on my test tomorrow. Any help will be appreciated

-
Try using a different value for $\Delta t$. – Emily Oct 31 '12 at 17:32
use $h=\Delta t = 0.1$ – user31280 Oct 31 '12 at 17:34
@F'OlaYinka: but the question specifically asked for $\Delta t=1$ – Ross Millikan Oct 31 '12 at 17:54
Actually, wait a second; where's the differential equation? – Emily Oct 31 '12 at 18:19
@EdGorcenski I was just wondering the same thing. – user31280 Oct 31 '12 at 18:22

Presumably the differential equation you are working with is $x'=-x$ with initial condition $x(0)=1$ and the capital $X$'s are the calculated points. You have done the iteration correctly, getting $x(1)=0$. Analytically we can see that the solution is $x=e^{-t}$, so the correct $x(1)=\frac 1e$. You could redo it with a smaller step size and see that it is more accurate, but that isn't asked for in the question.