Two applications dealing with the solutions of partial differential equations in two dimensions are examined, after a short review of the iterative relaxation methods used. The first example uses a slowly convergent but easy to parallelize algorithm. The second example adopts a more rapidly convergent method, but at the price of introducing data dependencies that invalidate the previous parallelization procedure. Different ways of coping with these data dependencies are explored, and different versions of the codes in the three programming environments—OpenMP, TBB, and vath—are also proposed. Their scalability properties as well as the impact of vectorization are examined.