Use Euler's Method with $\displaystyle h = 0.2$ to approximate the solution to the initial value problem:

$\displaystyle y' = -20y$

$\displaystyle y(1) = 3$

at

$\displaystyle x = 1, 1.2, 1.4$

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- Mar 3rd 2009, 06:29 PMArythEuler's Method
Use Euler's Method with $\displaystyle h = 0.2$ to approximate the solution to the initial value problem:

$\displaystyle y' = -20y$

$\displaystyle y(1) = 3$

at

$\displaystyle x = 1, 1.2, 1.4$ - Mar 4th 2009, 03:08 AMCaptainBlack
Euler's method for the numerical integration of an ODE IVP uses the stepping formula:

$\displaystyle y(t+ \delta t)=y(t)+\delta t\times y'(t)$

You are given $\displaystyle y(1)$ and that $\displaystyle \delta t =0.2$, so immediately the stepping formula will tell you the value at $\displaystyle t=1.2$, then applying it again from $\displaystyle t=1.2$ and the value of $\displaystyle y(1.2)$ you found from the first step, it will give the value at $\displaystyle t=1.4$.

CB - Mar 4th 2009, 05:25 AMAryth
I am getting bigger and bigger numbers... Is it supposed to blow up like that?

- Mar 4th 2009, 05:29 AMHallsofIvy
No, it shouldn't. Please show what you have done and why you are getting "bigger and bigger numbers".

- Mar 4th 2009, 05:36 AMCaptainBlack
- Mar 4th 2009, 05:48 AMAryth
Yeah. I knew the solution to the equation already.

Thanks for the help. I appreciate it. And this was a test question... I just wanted to get clarification on the answer.

But the next question was the same thing with the Improved Euler's method and I got a much better answer, which would mean that bigger values of h are allowed in the Improved method as opposed to the classical method. - Mar 4th 2009, 06:19 AMCaptainBlack