  A new method of numerical solution for partial differential equations is
proposed. The method is based on a fast matrix multiplication algorithm.
Two-dimensional Poison equation is used for comparison of the proposed method
with conventional numerical methods. It was shown that the new method allows
for linear growth in the number of elementary addition and multiplication
operations with the growth of grid size, as contrasted with quadratic growth
necessitated by the standard numerical methods. The proposed method can be
easily generalized for any differential equations.
