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Math Help - Finite difference problem

  1. #1
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    Finite difference problem

    Hi,
    Here is problem:

    Given that $ u_x $ is a polynomial of second degree and $ u_0=1,u_1+u_2=10,u_3+u_4+u_5=65 $


    Find the value of $ u_{10} $
    Solution:
    Now, here how should I make sub-division of intervals? i-e suppose we are given every nth value of a function and it is required to find out the values of the function at the

    individual points. e.g., the quinquennial values $ u_0,u_5,u_{10},u_{15},.....$ or decennial values $ u_0,u_{10},u_{20},u_{30},.... $are known and it is required to complete the

    series $ u_0,u_1,u_2,u_3,.....$ we can calculate $ \delta u_x, \delta u_x^2, \delta u_x^3 $ and so on
    Any hint to solve this problem is appreciated.
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  2. #2
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    Re: Finite difference problem

    Quote Originally Posted by Vinod View Post
    Hi,
    Here is problem:

    Given that $ u_x $ is a polynomial of second degree and $ u_0=1,u_1+u_2=10,u_3+u_4+u_5=65 $


    Find the value of $ u_{10} $
    Solution:
    Now, here how should I make sub-division of intervals? i-e suppose we are given every nth value of a function and it is required to find out the values of the function at the

    individual points. e.g., the quinquennial values $ u_0,u_5,u_{10},u_{15},.....$ or decennial values $ u_0,u_{10},u_{20},u_{30},.... $are known and it is required to complete the

    series $ u_0,u_1,u_2,u_3,.....$ we can calculate $ \delta u_x, \delta u_x^2, \delta u_x^3 $ and so on
    Any hint to solve this problem is appreciated.
    I'm not really sure what you are asking here. You have a 2nd order polynomial, i.e. 3 parameters, and a system of 3 equations. Simply solve for your parameters and use them to evaluate $u_{10}$

    I get

    Spoiler:
    $f(x)=x^2+x+1~~~~u_{10}=f(10)=111$


    What am I not understanding?
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  3. #3
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    Re: Finite difference problem

    Hi Romsek,
    I got answer to the problem.Your reply was helpful.
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