A new parallel algorithm for convection-dominated diffusion equation
is proposed. To derive an approximate solution of the problem at the same time level, we
use two domain decomposition methods. The average of the solutions obtained is set to
be new numerical solution. The algorithm demonstrates a high accuracy and is suitable
for parallel computing. Approximate solution of two-dimensional convection-dominated
diffusion equations is also considered. Numerical examples show the efficiency and reliability
of the algorithm.