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.

Use Euler's method with step size $10^{-n}$ for $n=1,2,3,4.$ to estimate $x(1)$, where $f(x)$ is the solution of the initial-value problem below.

$x'=f(x)=-x$

$x(0)=1$

EDIT / UPDATE:

x_n+1=x_n + f(x_n)h

how does it become x_n+1= x_n[(1-h)^(n+1)]

Solution then is X(1)=X_n where n=[1/h]

share|improve this question
    
Why not simply edit your previous question? –  Arkamis Oct 31 '12 at 19:32
1  
thanks, Khanak; reposting/editing keeps the problem/work altogether, in one location, and when you edit/answer a problem, it gets kicked up to the front of the "active" posts, so it won't get lost or overlooked. I'll add "EDIT" to your post, so those who have read the post previously see your update more readily.... –  amWhy Oct 31 '12 at 22:09

1 Answer 1

Euler's method is such:

$$ \begin{align*} x_0 &= x(0), \\ x_n &= x_{n-1}+hf(x_{n-1}). \end{align*}$$

For $h = 10^{-n}$, $x_{10^n} = x(1)$.

share|improve this answer

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.