Results 1 to 1 of 1

Thread: stability of heun method

  1. April 26th 2012, 02:32 AM #1
    psholder
    psholder is offline
    Newbie
    Joined
    Apr 2012
    From
    United States
    Posts
    4

    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.
    Follow Math Help Forum on Facebook and Google+
« Quasilinear parabolic equations with nonlocal boundary conditions | How do I write something as a first order system, or vector field, on the phase plane »

Similar Math Help Forum Discussions

  1. stability of solutions of an ODE?
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: July 9th 2011, 11:50 AM
  2. Proving Stability and Asymptotic Stability of Homogeneous Equations
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: November 4th 2010, 12:16 PM
  3. Mathematica Help (Beginner) - Euler's/Heun’s Method
    Posted in the Math Software Forum
    Replies: 0
    Last Post: December 2nd 2009, 07:42 PM
  4. Stability of a solution
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 12th 2007, 09:01 PM
  5. Stability
    Posted in the Advanced Applied Math Forum
    Replies: 0
    Last Post: January 17th 2007, 07:54 AM

Search Tags


/mathhelpforum @mathhelpforum