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Tridiagonal matrix solution,when inputs are three dimensional array

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ghasem_008

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hi.
I want to solve a tridiagonal equation system.as you know,form of a tridiagonal equation system is:
a(k)*x(k-1)+b(k)*x(k)+c(i)*x(k+1)=d(k)
that a,b,c are vectors (one dimensioal arrays).for example: a = [1 2 3 4 5]

but I have "three dimensional arrays" in input.i,e I have a(i,j,k),b(i,j,k),c(i,j,k),that I have to slove above tridiagonal matrix when k=i or j or k.
for example,when k=i (i=1:nx),index "j" and "k" have a loop for (j=1:ny, k=1:nz).
in fact,I want to slove tridiagonal matrix in 3D-ADI-FDTD.
can anyone help me?How should I act?
please give me a solution or instruction or algorithm in MATLAB?
best wishes...
 

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