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Solving Eulers Method

  1. Nov 3, 2011 #1
    Hi All,

    Just wanted to check to see if I am doing this correctly

    If the equation is

    [tex]F(t) = m\ddot{y}+c\dot{y}+ky[/tex]
    [tex]\dot{y}(0) = 0[/tex]

    Where m = 2, c =180, k=25, F(t) = -500sin(10t)

    I know that it has to be in the form of

    [tex]yk+1 = yk+f(xk,yk)h[/tex]

    So solving Eulers method to 0.2 with a step size of 0.1

    [tex] -500sin(10x)= 2\ddot{y}+180\dot{y}+25y[/tex]

    Now to change into for f(x,y) I have done the following

    [tex]f(x,y) = -500sin(10x)-2\ddot{y}-180\dot{y}-25y[/tex]

    Is this the correct equation for f(x,y)??

    So for i = 0

    [tex]yk+1 = yk+f(xk,yk)h[/tex]
    [tex]y1 = yo+f(xo,yo)h[/tex]

    x0 = 0
    y0 = 0
    h = 0.1

    This is where I think I have made a mistake becuase the two answers that I have found are very different from one another. I would like to know if I have done this correclty.

    [tex]y1 = 0 + f(0, 0)0.1[/tex]
    [tex]y1 = 0 + f(-500sin(10*0)-2*0-180*0-25 )*0.1[/tex]
    [tex]y1 = 2.5[/tex]

    and for i = 1

    [tex]y2 = y1+f(x1,y1)h[/tex]
    [tex]y1 = 1 + f(1, 1)0.2[/tex]
    [tex]y1 = 1 + f(-500sin(10*1)-2*1-180*1-25 )*0.2[/tex]
    [tex]y1 = -58.76[/tex]

    Have I used eulers method correctly to solve for y1 = -2.5, y2 = -58.76

    Thanks for your time
  2. jcsd
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