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Linear Algebra? (Or Differential Equation?)

  1. Apr 3, 2012 #1
    Find un, vn, and tn in terms of n for the following system:
    {
    un+1 = -un + 2vn + tn
    vn+1 = vn - tn
    tn+1 = 2tn

    For u0, v0, t0 given



    This isn't homework, it's on a study guide for my midterm.
     
  2. jcsd
  3. Apr 4, 2012 #2

    tiny-tim

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    welcome to pf!

    hi mudkip123! welcome to pf! :smile:

    you're looking for a combination an = Aun + Bvn + Ctn such that an+1 = Dan :wink:
     
  4. Apr 4, 2012 #3

    Ray Vickson

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    First solve the third one [itex]t_{n+1} = 2 t_n,[/itex] to get [itex] t_n = t_0 2^{n-1}.[/itex] Now look at the second one [itex] v_{n+1} = v_n -t_n.[/itex] It gives [itex] v_n = v_0 -\sum_{j=0}^{n-1} t_j, [/itex] which is computable. Now you have [itex] u_{n+1} = -u_n + f(n)[/itex] with a known function f(n), so you can solve it easily: [tex] u_1 = f(0)-u_0, \; u_2 = f(1) - u_1 = f(1)-f(0) + u_0, \; u_3 = f(2) - u_2 = f(2)-f(1)+f(0) - u_0, [/tex] etc.

    RGV
     
  5. Apr 4, 2012 #4
    This isn't in my linear algebra textbook so I don't know how to do this...
     
  6. Apr 4, 2012 #5

    micromass

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    You have been given enough hints. We will only help you further if you make an attempt now.
     
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