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Finding the coefficients of an unknown function using Taylor's Theorem?

  1. Sep 25, 2012 #1
    1. The problem statement, all variables and given/known data
    Find coefficients A, B, and C.
    f'(x)= Af(x)+Bf(x+h)+Cf(x+2h)+O(h2)
    Using Taylor's Theorem.

    Note: O stands for Big O in asymptotic order notation.



    3. The attempt at a solution

    Here are the expansions:

    Bf(x+h)= Bf(x)+Bhf'(x)+(1/2)Bh2f"(x)+(1/6)Bh3f"'(x)....

    Cf(x+2h)=Cf(x)+2Chf'(x)+2Ch2f"(x)+(4/3)Ch3f"'(X)...

    And then I added them and factored out the coefficients

    = (A+B+C)f(x)+(B+2C)hf'(x)+(1/2B+2C)h2f"(x)+....

    Is this correct? I'm stuck as to what I am supposed to do next.

    Thanks.
     
    Last edited: Sep 25, 2012
  2. jcsd
  3. Sep 25, 2012 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    That looks pretty odd. I think there is a typo in the problem. Try changing the left hand side from f'(x) to f'(x)*h. Now it makes a little more sense. Try it from there.
     
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