Results 1 to 6 of 6

Math Help - Linear Difference Equation

  1. #1
    Junior Member
    Joined
    Jan 2009
    Posts
    39

    Linear Difference Equation

    Ok I have a linear difference equation, which is as follows:
    f_t - f_(t+2) = 2sin(t*(pi/2))
    I am not given any conditions. All I am asked to do is solve it.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jan 2009
    Posts
    715
    f(t) = cos[(t-1)*pi/2] + k sin[pi*(t+w)] + c , c,k,w are constants
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Jan 2009
    Posts
    39
    Quote Originally Posted by simplependulum View Post
    f(t) = cos[(t-1)*pi/2] + k sin[pi*(t+w)] + c , c,k,w are constants
    I'm sorry, but that has completely confused me. I have solved the A.E. and the C.F, which turns out to be A(1)^t + B(-1)^t, but afterwards I get lost. I don't understand how you got that answer and would appreciate some more detail on how you arrived at it. Cheers
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Jester's Avatar
    Joined
    Dec 2008
    From
    Conway AR
    Posts
    2,325
    Thanks
    10
    Quote Originally Posted by LooNiE View Post
    Ok I have a linear difference equation, which is as follows:
    f_t - f_(t+2) = 2sin(t*(pi/2))
    I am not given any conditions. All I am asked to do is solve it.
    Is t an integer?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Jan 2009
    Posts
    39
    I believe t is an integer yes.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Apr 2005
    Posts
    14,974
    Thanks
    1121
    First solve f(t)- f(t+2)= 0 which is equivalent to [tex]f(t+2)= f(t). Try a solution of the form a^t so that f(t+2)= a^{t+2}= a^2a^t and the equation becomes a^2a^t= a^t so that a^2= 1 and a= 1 or a= -1. The general solution to the "associated homogenous equation" is C+ D(-1)^t exactly as you have.

    To find a specific solution to [tex]f(t)- f(t+2)= 2sin((\pi/2)t), try a solution of the form f(t)= A sin((\pi/2)t) so that f(2t)= A sin((\pi/2)(t+2))= A sin((\pi/2)t+ \pi)= -A sin((\pi/2)t) so the equation becomes f(t)- f(t+2)= 2A sin(\pi/2)t)= 2 sin((\pi/2)t) and is satisfied if A= 1.

    The solution is f(t)= C+ D(-1)^t+ sin((\pi/2)t).
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Solve Linear Difference equation
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: August 6th 2011, 01:39 AM
  2. Linear Difference Equation with Initial Conditions
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: March 24th 2011, 08:25 AM
  3. Linear Difference Equations
    Posted in the Advanced Algebra Forum
    Replies: 0
    Last Post: May 8th 2010, 10:59 AM
  4. Linear difference equations
    Posted in the Differential Equations Forum
    Replies: 2
    Last Post: March 31st 2009, 02:52 AM
  5. Replies: 1
    Last Post: May 15th 2008, 08:23 PM

Search Tags


/mathhelpforum @mathhelpforum