# Thread: Euler's method, no interval

1. ## Euler's method, no interval

I have a problem on which I need to apply Euler's method - EXCEPT that I don't have one of the crucial components. Question and my thoughts below:

**Question:** Consider the initial value problem $dy/dt=\alpha t^{\alpha - 1}, y(0)=0$, where $\alpha > 0$. The true solution is $y(t)=t^{\alpha}$. Use the Euler method to solve the initial value problem for $\alpha = 2.5,1,5,1.1$ with stepsize $h=0.2,0.1,0.05$. Compute the solution errors at the nodes, and determine numerically the convergence orders of the Euler method for these problems.

**My thoughts:** I don't have the "interval" for t! I tried setting the problem up as follows:

$0 \leq t \leq b$, with $N = (b-0)/0.2 = 5b$ for $h=0.2$, but wasn't able to get anything conclusive.

Should I try $b = 1$, so that t is restricted to a range in which it shrinks?

Thanks for any help.

2. ## Re: Euler's method, no interval

Hey abscissa.

You are right to ask questions about the interval: usually when you evaluating a function you need either a point or a range to evaluate.

If this is a homework question then you should ask your teacher to clarify this issue.