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Finite Difference

  1. Sep 17, 2006 #1

    Pyrrhus

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    Difference Equation

    Hello, can anyone offer any insight on this equation? . I am very very rusty on solving this type of equations.

    [tex] a_{n+1} - a_{n} = n^2 [/tex]
     
    Last edited: Sep 17, 2006
  2. jcsd
  3. Sep 17, 2006 #2
    Never even seen that one before :bugeye:
     
  4. Sep 17, 2006 #3

    0rthodontist

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    Use the method of undetermined coefficients.
    Homogeneous solution: C, a constant
    Particular solution: a quadratic in n
    multiply the particular by n so that it shares no terms with the homogeneous, and you get a cubic:
    an = An^3 + Bn^2 + Cn + D
    Then solve for A, B, C, D. You will need a base case.

    Edit: alternatively you could just look up the well-known formula for the sum of the first n squares.
     
    Last edited: Sep 17, 2006
  5. Sep 17, 2006 #4

    Pyrrhus

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    Thanks, exactly what i was looking for.
     
    Last edited: Sep 18, 2006
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