Below you can find a very brief description of the SOR and ESOR methods.
Successive Over-Relaxation (SOR / ESOR)
The (extrapolated) successive over-relaxation method is a variant of the Gauss–Seidel method for solving a system of linear equations A*x = b, where:
The extrapolated successive over-relaxation method is an iterative technique that, in the kth iteration, computes the elements of x(k+1) using the previous value x(k) as follows (until it converges):
By setting τ = w, we reach the well-known successive over-relaxation method:
ESOR method for tridiagonal system
The ESOR method can be used to solve a tridiagonal system A*x = d
In the kth iteration, the elements of x(k+1) are computed as follows:
which is easily depicted from the original ESOR formula given the special structure of the A matrix (tridiagonal).