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 , where . The true solution is . Use the Euler method to solve the initial value problem for with stepsize . 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:
, with for , 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.
Re: Euler's method, no interval
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.