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Math Help - Euler's method, no interval

  1. #1
    Junior Member
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    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.
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  2. #2
    MHF Contributor
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    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.
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