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Math Help - central difference scheme

  1. #1
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    central difference scheme

    I need a little clarification about how to use this equation.

    f'(x)=f(x+h)-f(x-h)/2h + O(h^2)


    here is the info
    time___ 0 20 40 . . . . . . . . . . . .......................... . . 160 180 200
    altitude 60 10170 33835 ........................107892 119626 162095

    find the central difference at t=20 and t=180

    I know how to find h but how to i put all these x values into the equation?
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  2. #2
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    Quote Originally Posted by calculushelptx View Post
    I need a little clarification about how to use this equation.

    f'(x)=f(x+h)-f(x-h)/2h + O(h^2)


    here is the info
    time___ 0 20 40 . . . . . . . . . . . .......................... . . 160 180 200
    altitude 60 10170 33835 ........................107892 119626 162095

    find the central difference at t=20 and t=180

    I know how to find h but how to i put all these x values into the equation?
    Then presumably you saw that h= 20. So just put the numbers into the equation. With x= 20 and h= 20, x+h= 40 and x- h= 0. f(x-h)= f(0)= 60 while f(x+h)= f(40)= 33835. (f(x+h)- f(x-h))/(2h)= (f(40)- f(0))/(2(20))= (33835- 60)/60.
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  3. #3
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    (f(x+h)- f(x-h))/(2h)= (f(40)- f(0))/(2(20))= (33835- 60)/60.
    Liitle mistake here, should be (33835 - 60)/(40)

    And O(h^2) is the error you make, cause you are calculating a numerical approximation.
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  4. #4
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    Quote Originally Posted by jeneverboy View Post
    Liitle mistake here, should be (33835 - 60)/(40)

    And O(h^2) is the error you make, cause you are calculating a numerical approximation.
    Yes, of course. Thank you for the correction.
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