This paper is a brief story about the theory of Local Recursive non-Local Asynchronous (LRnLA) algorithms - a new efficient tool for solving problems, self-consistent model describing a system of hyperbolic equations, linear and nonlinear, on current and future computers. Features of the algorithm are shown on the examples of the solution of particular problems of plasma physics, nanophysics, seismic and a number of others.

Mathematical modelling in actual problems of science and technics