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Math Help - Improved Euler's Method Help

  1. #1
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    Question Improved Euler's Method Help

    I am trying to use the Improved Euler's Method to solve a homework problem, but I am having trouble with the notation and my book is extremely unhelpful.


    Where the lower formula is the Improved Euler's method.

    I am given:

    y = 5e^(x(x+2))
    y' = 2y(x+1)
    y(0) = 5
    dx = .3 (I'm guessing this is step size...)

    My main difficulty is notation and conception of the problem: the notation is confusing me, and I'm not sure what is actually happening in the formula. Does f(x,y) mean the function with x and y substituted, or something else? The problem asks for the first approximation. If someone could explain the problem in steps that would be great.
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  2. #2
    Senior Member
    Joined
    Jul 2006
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    Usually they tell you that y'=f(x,y).

    So in your case f(x,y)=2y(x+1) and y_0=y(x_0)=5 and x_0 = 0.

    So find z_1 and then y_1, x_1, then z_2, y_2, x_2, etc.

    They should probably mention that x_n = x_{n-1}+\Delta x

    (Usually h is used for the step size though.)
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