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Math Help - numerical analysis...

  1. #1
    Newbie
    Joined
    Dec 2008
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    1

    numerical analysis...

    Derive the Adams-Bashforth (AB) method for the following problem using the interpolationg polynomial of degree 2.( Explicit multi-step method )

    Y'(x)=f(x,Y(x)) on x>0
    Y(0)=Y lower case 0

    Derive the Adams-Moulton (AM) method for the same problem using the interpolationg polynomial of degree 2.( Implicit multi-step method )


    can anyone help me with this problem??
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  2. #2
    Senior Member
    Joined
    Mar 2009
    Posts
    378
    I know this is late, but what you want to do is setup the following
    y' = f(t,y) \Rightarrow \int_{t_k}^{t_{k+1}}\! y' \, dt = \int_{t_k}^{t_{k+1}}\! f(t,y) \, dt \Rightarrow y_{k+1} = y_k + \int_{t_k}^{t_{k+1}}\! f(t,y) \, dt

    For Adams-Bashforth interpolate f(t,y) at the points t_{k-2}, t_{k-1}, t_{k} using the Lagrange interpolating polynomial and then integrate.

    For Adams-Moulton interpolate f(t,y) at the points t_{k-1}, t_k, t_{k+1} using the Lagrange interpolating polynomial and then integrate.
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