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Second order O.D.E

  1. Apr 27, 2012 #1
    Please see the attached description of the problem


    I need to split the second-order o.d.e to two first-order o.d.e's.
    (numerically)

    Then use the shooting method with a 0.5 step size to solve the system of equations.
    (This needs to be done on an excel spreadsheet)

    Then to plot the temperature along the body.
    (not sure how to do this)

    I don't know where to start! Can anyone help!
     

    Attached Files:

  2. jcsd
  3. Apr 27, 2012 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Your second order ODE is
    [tex]\frac{d^2T}{dx^2}+ a(x)\frac{dT}{dx}+ b(x)T= f(x)[/tex]

    Let S(x)= dT/dx and that becomes
    [tex]\frac{dS}{dt}+ a(x)S+ b(x)T= f(x)[/tex]
    so your two first order equations are
    [tex]\frac{dS}{dx}= -a(x)S- b(x)T+ f(x)[/tex]
    [tex]\frac{dT}{dx}= S[/tex]
     
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