Аннотация: A new difference scheme is proposed with increased (fourth)order of accuracy for Poisson's equation in a p-dimensional parallelepiped having the strong elliptic property for any p ≥ 2. For the solution iterative methods of variable directions are applied, and the alternate-triangular method with Chebyshev and cyclic families of parameters. Comparison with early proposed methods shows that the methods considered here significantly diminish the number of iterations necessary for obtaining the desired accuracy.