three coupled equations

ptub · February 20, 2016, 14:32

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.

FMDenaro · February 20, 2016, 14:59

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

ptub · February 20, 2016, 15:04

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.

FMDenaro · February 20, 2016, 15:29

Quote:

Originally Posted by ptub

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?

ptub · February 20, 2016, 15:38

Quote:

Originally Posted by FMDenaro

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.

FMDenaro · February 21, 2016, 13:33

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

February 20, 2016, 14:32	three coupled equations	#1
ptub New Member Join Date: Dec 2015 Posts: 6 Rep Power: 10	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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February 20, 2016, 14:59		#2
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,882 Rep Power: 73	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

February 20, 2016, 15:04		#3
ptub New Member Join Date: Dec 2015 Posts: 6 Rep Power: 10	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.

February 21, 2016, 13:33		#6
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,882 Rep Power: 73	Check for an interative splitting method so that you can work with iterated Thomas solver