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

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The discussion centers on the occurrence of negative coefficients in the matrix equation Ax = b while solving partial differential equations related to transient advection and diffusion. Users confirm that negative coefficients are typical, especially when using finite difference methods, where patterns such as -1, 2, -1 are common for second derivatives. The presence of negative values does not indicate an error in the calculations or code, but rather reflects the mathematical properties of the numerical methods employed.

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  • Familiarity with finite difference methods for solving partial differential equations
  • Basic knowledge of transient advection and diffusion processes
  • Experience with numerical analysis and error analysis in computational methods
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Researchers and practitioners in chemistry, applied mathematics, and engineering who are involved in numerical simulations of physical processes, particularly those using finite difference methods for solving differential equations.

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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!
 
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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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