Modern methods of direct numerical simulations of transfer processes in random media

Abstract The paper considers the methods of direct numerical investigation behaviour dynamical systems explosive type under influence random noise. Dynamical are described by a system nonstationary ordinary differential equations (ODE). dynamics system, taking into account noise, is stochastic (SODE). provides an overview modern algorithms based on modifications Runge – Kutta integration methods. features analysis weak and strong convergence SODE described. Methods for generating noise with complex temporal structure (color noise) method solution used to generate color Examples study biological mechanical presented. It shown that noises acting such qualitatively change character their behaviour.