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Forward substitution in this case? Is it as simple as I think it is?

  1. Jan 28, 2010 #1
    Hi everyone:

    I am very rusty on linear algebra, so apologies if this is a silly question. The question is, in the system below, is it correct to take the calculated value of uik+1 from each PREVIOUS step and simply plug it in at the NEXT step where (a * ui-1k+1 is required.

    I need to incorporate a finite difference calculation for 1-dimensional advection in some code I'm writing. I have derived the system of equations that I need, but my linear algebra is so rusty that I'm stuck on what to do next/how to actually use them. I'm hoping that the solution I proposed will be sufficient. If it isn't, what method from linear algebra should I use?

    I would very much appreciate any help. Thank you all.

    Here is the system (a and d are constants that I can specify):

    u1k+1 = (u1k - a(0, tk+1)/d

    u2k+1 = (u2k - a(0, u1k+1)/d

    uik+1 = (uik - a(0, ui-1k+1)/d
    Last edited: Jan 28, 2010
  2. jcsd
  3. Jan 29, 2010 #2


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    Science Advisor

    Yes, that is a standard technique.
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