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Old   February 20, 2016, 14:32
Red face three coupled equations
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Hi,

I am trying to solve three coupled equations in 1D computational domain. For example, if I want to write my first equations, there are six unknowns a(i+1), a(i), a(i-1) ,c(i-1) c(i),c(i+1). and so for second and third equation. However, I couldn't get tri-diagonal matrix I didn't get how to set my unknowns into matrix. Can somebody help? Thanks.
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Old   February 20, 2016, 14:59
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But it is a problem for you if the matrix is not tri-diagonal?
your unknown vector x is something like this?

A.x=q

x=
[a(1),...a(N), b(1), ....b(N), c(1),....c(N)]^T
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Old   February 20, 2016, 15:04
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Yeap. My first equation for a(1) includes unknowns C(1) and C(2). Also b(1) includes C(1) and C(2). C(1) includes A(1) and B(1). At the end, I didn't get tri-diagonal matrix. I had tri-diagonal matrix solver. I don't have sparse matrix solver. I am not sure how to proceed.
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Old   February 20, 2016, 15:29
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Quote:
Originally Posted by ptub View Post
Yeap. My first equation for a(1) includes unknowns C(1) and C(2). Also b(1) includes C(1) and C(2). C(1) includes A(1) and B(1). At the end, I didn't get tri-diagonal matrix. I had tri-diagonal matrix solver. I don't have sparse matrix solver. I am not sure how to proceed.
Have you tried to organize a block-matrix form?
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Old   February 20, 2016, 15:38
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Quote:
Originally Posted by FMDenaro View Post
But it is a problem for you if the matrix is not tri-diagonal?
your unknown vector x is something like this?

A.x=q

x=
[a(1),...a(N), b(1), ....b(N), c(1),....c(N)]^T
I am not sure how to do that. If I do that, my unknown matrix won't be like this x.
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Old   February 21, 2016, 13:33
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Check for an interative splitting method so that you can work with iterated Thomas solver
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