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Stability criteria of heat-like equation

  1. Nov 9, 2014 #1
    I know that the criterion of stability for an explicit solution to the heat equation:

    [itex]\frac{\partial T}{\partial t}=D\frac{\partial^2 T}{\partial x^2}[/itex]
    [itex]\Delta t <\frac{1}{2}\frac{\Delta x^2}{D}[/itex]

    however, what is the stability criterion for an equation of the form

    [itex]\frac{\partial T}{\partial t}=D\frac{\partial^2}{\partial x^2}\left(\frac{T}{P(D)}\right)[/itex]

    where P(D) indicates that P depends on the value of D, which varies arbitrarily in space.

    I would like to solve this equation with explicit finite differences, so I will have a term of the form:

    [itex]\frac{\partial T}{\partial t}=\frac{D+D_L}{2 \Delta x^2}(\frac{C_L}{P_L}-\frac{C}{P})+\frac{D+D_R}{2\Delta x^2}(\frac{C_R}{P_R}-\frac{C}{P})[/itex]

    where subscripts L and R indicate relative position (left and right of the point of calculation).

    How can I figure out the maximum timestep allowed.
  2. jcsd
  3. Nov 14, 2014 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
  4. Nov 17, 2014 #3
    You want to use something call Von Neumann Stability analysis.
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