tridiagonol matrice
 

Can someone explain how to solve a two dimensional tdma problem?

You will find the algorithm for TDMA in a few books:

J. D. Anderson - Introduction to CFD
Tletcher - Computational Techniques for Fluid Dynamics

and obviously Wikipedia (even with an implementation example):

http://en.wikipedia.org/wiki/Tridiag...trix_algorithm

here you will see how to use TDMA to solve a linear equation line by line:

http://www.stanford.edu/class/me469a...lvers/lapl2d.f

Do

I think what you want is algorithm for block tridiagonal system. You should look into blktri method of fishpack.