# Euler's method, no interval

• Nov 15th 2013, 06:03 PM
abscissa
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 $\displaystyle$dy/dt=\alpha t^{\alpha - 1}, y(0)=0$$, where \displaystyle \alpha > 0$$. The true solution is $\displaystyle$y(t)=t^{\alpha}$$. Use the Euler method to solve the initial value problem for \displaystyle \alpha = 2.5,1,5,1.1$$ with stepsize $\displaystyle$h=0.2,0.1,0.05$$. Compute the solution errors at the nodes, and determine numerically the convergence orders of the Euler method for these problems. **My thoughts:** I don't have the "interval" for t! I tried setting the problem up as follows: \displaystyle 0 \leq t \leq b$$, with $\displaystyle$N = (b-0)/0.2 = 5b$$for \displaystyle h=0.2$$, 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.
• Nov 15th 2013, 09:09 PM
chiro
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.