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

Abstract

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