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Math Help - Matlab 2nd order methods

  1. #1
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    Sep 2008
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    7

    Matlab 2nd order methods

    This is the question I have

    Let f(x) be a given function which can be evaluated at any point. In the following question, h refers to the step size or the distance between the equally spaced points used in the approximation.
    Find a 2nd order method (i.e., truncation error O(h2)) approximating
    f′′′(x0).
    Give the formula as well as an expression for the truncation error. Hint: You may want to consider the Taylor expansions of f(x0 h) then f(x0 2h). It is easier to consider each of these cases separately, then combine the results.

    I'm just looking for a start or some sort of M-file to get me going on the rest of the stuff. I know the taylor expansions for f(x+h),f(x-h),f(x+2h),f(x-2h) but im not sure how to comebine them to make this work. I know I have to get this and then plug different h's in to see the difference in error.

    Please help.

    Thank you very much.
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  2. #2
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    Joined
    Sep 2008
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    7
    I expanded the functions in the taylor and got

    y(x+h) = y(x) + hy'(x) + h^2/2*y"(x) + h^3/6y"'(x) + h^4/12*O(h^4)

    y(x+h) = y(x) - hy'(x) + h^2/2*y"(x) - h^3/6y"'(x) + h^4/12*O(h^4)

    y(x+2h) = y(x) + 2hy'(x) + h^2*y"(x) + h^3/3y"'(x) + h^4/6*O(h^4)

    y(x+2h) = y(x) - 2hy'(x) + h^2*y"(x) - h^3/3y"'(x) + h^4/6*O(h^4)

    im not sure if i went too far or what. please help
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