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Matrix equation: Ax=b; can A coefficients be negative? Or could this be error?

  1. Oct 20, 2011 #1
    Hello all:

    I'm using a code for solving partial differential equations that describe transient advection and diffusion.

    I'm more of a chemistry person, so I'm a bit lost on some of the basics of the calculation method.

    A general question:

    As my calculation progresses, I see that some of the A coefficient values (in the equation Ax = b) go negative. This seems weird because all of the values used in the problem represent measurements that I carried out in my lab (positive).

    So I'm trying to figure out whether there is some mathematical reason (like error? Something else I haven't thought of?) why these negative values may be arising or whether there is a bug in the code. I'm not sure if I have provided enough information for anyone to speculate, but I'd be interested in hearing any suggestions. Thanks a lot!
  2. jcsd
  3. Oct 20, 2011 #2


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    Science Advisor
    Homework Helper

    Assuming you are using some sort of finite difference solution, the coefficients representing a second derivative will form a pattern that looks like -1, 2, -1.

    So negative coefficients in the matrix are prefectly normal, and they won't cause any numerical problems.
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