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Thread: 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
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    Usually they tell you that $\displaystyle y'=f(x,y)$.

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

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

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

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