In this paper, three-dimensional parabolic and pseudo-parabolic equations with classical, periodic and nonlocal boundary conditions are approximated by the full approximation backward Euler method, locally one dimensional and Douglas ADI splitting schemes. The stability with respect to initial conditions is investigated. We note that the stability of the proposed numerical algorithms can be proved only if the matrix of discrete operator can be diagonalized and eigenvectors make a complete basis system.
Parallel versions of all algorithms are constructed and scalability analysis is done. It is shown that discrete one-dimensional problems with periodic and nonlocal boundary conditions can be efficiently solved with similar modifications of the parallel Wang algorithm.