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Runge kutta method for solving PDE

  1. Apr 4, 2008 #1
    Hi!
    If you don't see clearly this n terms please download the word file attached here.
    Am a given a problem like f(x,y,y')= y''= x+y with y(0)=0, y'(0)=1 and h=0.1 and i want to solve it using Ringe Kutta.
    As we know y_(n+1)= y_n + h(y'_n+(A_n + B_n + C_n)/3)
    And y'_(n+1) = y'_n+(A_n + 2B_n + 2C_n + D_n)/3
    x_(n+1)=x_0+(n+1)h
    where
    k=h/2
    A_n=kf(x_n,y_n,y'_n)
    [tex]\beta[/tex]_n= k(y'_n+(1/2)A_n) and so for
    B_n=kf(x_n +k,y_n + [tex]\beta[/tex]_n,y'_n + A_n)
    C_n= kf(x_n + k, y_n + [tex]\beta[/tex]_n, y'_n + B_n)
    [tex]\delta[/tex]_n=h(y'_n + C_n)
    D_n=kf(x_n +h, y_n + [tex]\delta[/tex]_n,y'_n + 2 C_n)
    My problem is this:
    For that given function(above) we can see that the y'_n ,i.e the third term in the brackets, is useless in the funtion. So i all the calculations the third term will be neglected. First tell me if i am right or not!
    I did like that but during the class, the lecturer took the third term into account and add it to both x + y with reasons that only y'_n is zero but the third term will not be always zero because it contains the sums of A_n which is not zero.
     

    Attached Files:

  2. jcsd
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