three coupled equations
 

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.

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

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?

I am not sure how to do that. If I do that, my unknown matrix won't be like this x.

Check for an interative splitting method so that you can work with iterated Thomas solver