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Homework Help: Numerical Analysis Euler's Method

  1. May 5, 2010 #1
    Please help me with this problem! I have no clue. I know how to deal with only dy/dx. But this includes dy/dx and dz/dx....:cry:
    Please see the attachment :)

    Step size h = 0.2
    range x = 0 to 1
    y(0) = 2
    z(0) = 4

    Thank you,
    Maya
     

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  3. May 5, 2010 #2

    vela

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    What don't you get?
     
  4. May 5, 2010 #3

    HallsofIvy

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    Just do two Euler calculations.

    Since the d.e. are
    [tex]\frac{dy}{dx}= -2y+ 4e^{-x}[/tex]
    and
    [tex]\frac{dz}{dx}= -\frac{yz^2}{3}[/tex]

    use the given initial values x= 0, y= 2, and z= 4 to calculate the two right sides:
    [tex]\frac{dy}{dx}= -2(2)+ 4e^{0}= -4+ 4= 0[/tex]
    and
    [tex]\frac{dz}{dx} -\frac{(2)(16){3}= \frac{32/3}= -10.66666...

    Since h= .2, x= 0+ h= 0+ .2= .2, y= 2+ (dy/dx)h= 2 - 0= 2, z= 4+ (dz/dx)h= 4- 2.133333= 1.8666668.

    and repeat.
     
  5. May 6, 2010 #4
    thanks sooooo much! i've got it!!!
    :rofl:
     
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