A divide-and-conquer algorithm for the resolution of distributed linear tridiagonal systems of equations is implemented within a binary tree connection architecture. A new scheme for the distribution of the data among the computing nodes allows a dilation-one implementation of a recursive substitution scheme for the solution of the global system. In this way, computation time decreases linearly with the number of nodes, and the data communication required becomes proportional to the logarithm of the number of nodes. This takes place within a network with a fixed connectivity degree of three.