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Partial differential equation discretization. HELP! D:

  1. Feb 4, 2014 #1
    So figuratively, I'm trying to win a nuclear war with a stick. :rofl: I did not take any course in PDEs, I just self-studied some of them, and now I'm toast. :rofl:

    First, please feel free to hurl rocks at me if my simplification is incorrect:

    https://fbcdn-sphotos-g-a.akamaihd.net/hphotos-ak-prn2/t1/q71/1545789_719161698116788_1463986171_n.jpg

    Second, how do you discretize ∂2u/(∂x∂y)? Is it:

    (ux+1,y - 2ux,y + ux-1,y)(ux,y+1 - 2ux,y + ux,y-1)/((xi+1 - xi)(yi+1 - yi))

    I might have a few more questions after this. Sorry if everything I'm saying is incorrect, please don't be harsh. I'm telling the truth when I say that we didn't cover this in our numerical methods class and I didn't take a PDE course. Thanks!
     
  2. jcsd
  3. Feb 11, 2014 #2
    First:
    Your equations looks right as long as [itex] \mu [/itex] does not depend on x…
    (If [itex] \mu [/itex] does depend on x, they might still be a decent approximation if [itex] \mu [/itex] does not vary much, but I don't know what problem you are working on... )

    Second:

    Last section of: http://en.wikipedia.org/wiki/Finite_difference . ;)

    I don't have any PDE courses either, so not sure exactly how to derive it. I think you can derive it straight from the definiton of the taylor series of a function of two variables and dropping higher order terms :)
     
    Last edited: Feb 11, 2014
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