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Math Help - diff. eq.

  1. #1
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    diff. eq.

    Hey Guys,
    Can you help figure out how to set up excel to solve this, or a way to calculate it by hand?


    Calculate the first 3 terms of the RK-2 (improved euler) solution of the differential equation:

    y' = y - x when y(1) = 1



    n = 0, Xn = 1, Yn = 1, Yn+1 = ?

    n = 1, Xn = 1.1, Yn =?, Yn+1 = ?

    n = 2, Xn = 1.2, Yn =?, Yn+1 = ?
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  2. #2
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    Quote Originally Posted by boousaf View Post
    Hey Guys,
    Can you help figure out how to set up excel to solve this, or a way to calculate it by hand?


    Calculate the first 3 terms of the RK-2 (improved euler) solution of the differential equation:

    y' = y - x when y(1) = 1



    n = 0, Xn = 1, Yn = 1, Yn+1 = ?

    n = 1, Xn = 1.1, Yn =?, Yn+1 = ?

    n = 2, Xn = 1.2, Yn =?, Yn+1 = ?
    Here you have y'=f(x,y)=y-x

    You need to set up the spread sheet with columns:

    Code:
       n      x_n       y_n        f(x_n,y_n)     k1_n=h*f(x_n,y_n)    k2_n=f(x_n+h/2,y_n+k_1/2)
       0       1         1             0                0                        1+h/2  
       1   x_{n-1}+h  y_n+k2_{n-1}              ...  etc
    After the first row the second column is set equal to the seventh column of the preceeding row.

    You put h in some cell away from the table so references to h above are to that cell

    RonL

    RonL
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  3. #3
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    ty kindly!
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