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Thread: stability of heun method

  1. #1
    Apr 2012
    United States

    stability of heun method

    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

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

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

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

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

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

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

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