Results 1 to 5 of 5

Math Help - Finding Function for a recurrance relation

  1. #1
    Junior Member
    Joined
    Feb 2008
    Posts
    48

    Finding Function for a recurrance relation

    I need help find a function for the following recurrence relation

    h _{n}=2*h _{n-1}+2*h _{n-2}

    It's getting to big and messy for me to recognize any pattern.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    I am assuming you have some initial condtions?. Something like

    h_{n}=0, \;\ h_{1}=1 or something like that.

    You can write it as h^{2}-2h-2=0

    Solving, we see h=\sqrt{3}+1, \;\ h=1-\sqrt{3}

    Then, h_{n}=a(\sqrt{3}+1)^{n}+b(1-\sqrt{3})^{n}

    Now apply your initial condtions to find a and b.
    Last edited by galactus; March 17th 2008 at 03:12 PM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Feb 2008
    Posts
    48
    h _{1}=3
    h _{2}=8
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    In that event, you have two equations to solve for a and b. Just use your conditions.

    a(\sqrt{3}+1)+b(1-\sqrt{3})=3

    a(\sqrt{3}+1)^{2}+b(1-\sqrt{3})^{2}=8
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by hockey777 View Post
    I need help find a function for the following recurrence relation

    h _{n}=2*h _{n-1}+2*h _{n-2}

    It's getting to big and messy for me to recognize any pattern.
    This is a linear constant coefficient homogeneous difference equation. You treat it like a linear constant coefficient homogeneous ODE.

    Take trial solution h_n=\mu^n, substitute this into the recurrence to get a quadratic equation for \mu. Solve the quadratic to get two basic solutions, form a general solution as a linear combination of these two solutions.

    RonL
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] limits of recurrance relation, log(a+b)
    Posted in the Calculus Forum
    Replies: 2
    Last Post: October 9th 2011, 11:24 AM
  2. Prove recurrance relation
    Posted in the Differential Equations Forum
    Replies: 9
    Last Post: December 15th 2010, 05:52 PM
  3. Recurrance Relation
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: November 14th 2010, 11:52 PM
  4. recurrance relation
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 13th 2009, 06:33 PM
  5. Solving recurrance relation using any technique
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: June 1st 2008, 05:11 AM

Search Tags


/mathhelpforum @mathhelpforum