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Math Help - stability of heun method

  1. #1
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    stability of heun method

    Hey,
    I'm trying to determine the region of stability for the Heun method and whether it is A stable. I've looked at the examples on wiki here Stiff equation - Wikipedia, the free encyclopedia and Runge here. By plugging in the test equation y' = zy where k is complex I've simplified the Heun algorithm from

    $$y_{n+1} = y_n + 0.5\cdot h\bigl(f(t_n, y_n) + f(t_{n+1},y_n + 0.5\cdot h\cdot f(t_n, y_n)\bigr)$$

    then when I insert $y' = zy$ for $f(t,y)$, my result simplifies to


    $$ y_{n+1} = (0.25\cdot h^2 \cdot z^2 + hz + 1)y_n $$


    to judge from the wiki article, the stability region is then the area described by


    $$\\{z \in \mathbb C \mid 0.25h^2z^2 + hz + 1 < 1\\}$$


    Am I on the right path at all? How does this relate to A stability? Appreciate any help.





    Last edited by psholder; April 26th 2012 at 02:35 AM.
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