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Thread: ODE

  1. #1
    Nov 2009

    Second order ODE problem help needed...:)

    Hi guys, I have the following problem and I dont know how to start.

    I am given that W = 0.5, X(0) = 0, $\displaystyle \frac{dy}{dx}=0$


    \frac{dy^2}{d^2x}=\frac{W}{T}\sqrt{1 + (\frac{dy}{dx})^2}

    I am told to convert the 2nd order ODE to two 1st order ODEs so what I did is:

    $\displaystyle \frac{dy}{dx}=g$ and $\displaystyle \frac{dg}{dx}=\frac{W}{T}\sqrt{1 + g^2}$

    i am then asked to choose an arbitrary value of T and integrate the system of equations using Euler's method from 0-Iab, where Iab=20, with 3 different step sizes. So, what I did was:

    $\displaystyle yi+1 = yi + gi*h$ and $\displaystyle gi+1 = gi + (\frac{W}{T}\sqrt{1+gi^2})*h$

    My problem is, I dont know where to start in order to find y(Iab) (because the problem is asking for an accurate value of y(Iab) )... and what step size (h) to use. It is asking me to do calculations with 3 different step sizes and select the step size that gives an accurate value of y(Iab) (i.e. approximate relative error less than 0.1% if comparing with ha = 5)..

    any help would be really appreciated. thank you
    Last edited by meddi83; Nov 26th 2009 at 02:03 PM. Reason: mistakes..:)
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