Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

$f(x)=-x$ 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

share|improve this question
    
Try using a different value for $\Delta t$. –  Arkamis 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
4  
Actually, wait a second; where's the differential equation? –  Arkamis Oct 31 '12 at 18:19
    
@EdGorcenski I was just wondering the same thing. –  user31280 Oct 31 '12 at 18:22
add comment

1 Answer

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.

share|improve this answer
    
+1 for simply interpreting the question :-) (and for a good answer) –  robjohn Oct 31 '12 at 20:02
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.