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Math Help - Euler's Method - Global Error

  1. #1
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    Euler's Method - Global Error

    Use Euler's method with h = 1/2 to estimate y(1) for the IVP:

    y(0)=1

    y'(t)=t^2-y(t)

    Assuming that |y(t)| \le 1 for 0 \le t \le 1 determine the value of n needed to ensure that |E_n| \le 10^{-2}

    The first part is easy enough:

    y_1=y_0+f(t_0,y_0)h=1+f(0,1)(1/2)=1/2

    y_2=y_1+f(x_1,y_1)h=1/2-1/8=3/8

    \Rightarrow y(1)=3/8

    I'm having trouble with the second part. I know I need to use:

    |E_n|\le \frac{T}{L}\left(e^{L(t_n-t_0)}-1\right)

    Could somebody explain to me how I find L and T?
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  2. #2
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    Re: Euler's Method - Global Error

    Is this correct for L:

    |f(t,u)-f(t,v)|=|t^2-u-t^2+v|=|u-v|

    Lipschitz with L=1
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  3. #3
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    Re: Euler's Method - Global Error

    It's T that I'm having trouble with... how would I find the upper bound for |y''(t)| ?
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