Solving a system of tirdiagonal matrices

[hoomanya]

Hi,

I am trying to solve a system consisting of tridigonal matrices and looks like this:

v1(1,4) ^{n+1}= v1(1,4) ^{n} + \Deltat* [ tridiagonal(4,4)*v1(1,4) + tridiagonal(4,4)*v2(1,4) ]^{n}

v2(1,4) ^{n+1}= v2(1,4) ^{n} + \Deltat* [ tridiagonal(4,4)*v2(1,4) + tridiagonal(4,4)*v1(1,4) ]^{n}

when n is the time step number. \Deltat is the time step. and x(1,4) means a matrix with 1 column and 4 rows.

I have boundary conditions at t=0, v1 = v2 = 0. And at any other time v1(1) = 0 and v2(4) = 1.

I have seen methods on solving tridiagonal matrices but been struggling to find one like this.. Please help!!!

Cheers!!