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Math Help - Checking Taylor Expansions

  1. #1
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    Checking Taylor Expansions

    Hi, I just want to check that I have the Taylor expansions correct for these choices.
    I cannot find any examples on the net. So would be great if you could give me these.
    y(x_{i+1})
    y(x_{i+2})
    y'(x_{i-2})
    y'(x_{i+1})

    Thanks in advance
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  2. #2
    A Plied Mathematician
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    I think we're missing an awful lot of information here. What is y? Where are your x_{i}'s?
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by james12 View Post
    Hi, I just want to check that I have the Taylor expansions correct for these choices.
    I cannot find any examples on the net. So would be great if you could give me these.
    y(x_{i+1})
    y(x_{i+2})
    y'(x_{i-2})
    y'(x_{i+1})

    Thanks in advance
    Post the actual question please.

    CB
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  4. #4
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    Quote Originally Posted by Ackbeet View Post
    I think we're missing an awful lot of information here. What is y? Where are your x_{i}'s?
    Hi, for example a solution could be:
    y(x_{i+1})=y(x_{i})+hf'(x_{i})+((h^2)/2!)*f''(x_{i}) (not sure if this is correct)
    where h=x_{i}-x_{i-1} and x_{i} is a general point.

    Thanks
    James
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  5. #5
    A Plied Mathematician
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    Ok, so it looks like you're trying to construct an iterative sequence out of the Taylor series expansion for a function. Is that correct? If so, where do you want to expand the Taylor series? It matters where you're trying to expand the series.
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  6. #6
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    Quote Originally Posted by Ackbeet View Post
    Ok, so it looks like you're trying to construct an iterative sequence out of the Taylor series expansion for a function. Is that correct? If so, where do you want to expand the Taylor series? It matters where you're trying to expand the series.
    The actual question I am asked is:
    Find the principle local truncation error and the order of Quade's method
    y_{n+1}-8/19*(y_{n}-y_{n-2})-Y_{n-3}=6/19*h*(y'_{n+1}+4y'_{n}+4y'_{n-2}+y'_{n-3})

    And the idea is to use the Taylor series and cancel out to get the error. So I assume it is around x=0.


    Thanks
    James
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  7. #7
    A Plied Mathematician
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    Couple comments:

    1. I assume the last term on the LHS is meant to be lower-case.

    2. In googling Quade's method (which I've never heard of before), I saw at least one definition of it that has different indices than yours. Here's one such example. I don't know if it's correct or not. There seem to be multiple definitions of the method out there.

    I'm out of my league here. CB, what do you think?
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