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Shooting Method

  1. Mar 31, 2006 #1
    dy/dt = ky, where k is a constant.
    y|t=0 = 1; y|t=10 = 4

    I need to approximate k using the shooting method and Euler's method... plz help.. :)

    wat's the procedure to approximate k using the shooting method :confused:
     
  2. jcsd
  3. Apr 4, 2006 #2

    HallsofIvy

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    Do you know what "Euler's method" is?

    Start with an easy estimate: take dt= 5 so we have only two steps
    Initially, t= 0, y= 1, so dy/dt= k and dy= 5k

    then t= 5, y= 1+ dy= 1+ 5k so dy/dt= k(1+ 5k)= k+ 5k2 and so dy= 5(k+ 5k2)= 5k+ 25k2.

    Finally, then, x= 10, y= 1+ 5k+ dy= 1+ 5k+ 5k+ 25k2= 1+ 10k+ 26k2= That is, 25k2+ 10k- 3= 0. Solve that for k.

    Now that you know, roughly, k, use, say, 10 steps from x= 0 to x= 10 with that k and see if you get 4 there. You won't of course, but that will tell you whether to make k smaller or larger. Do that repeatedly until you get a good method.
     
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