This article is cited in 2 papers

MATHEMATICAL MODELING AND NUMERICAL SIMULATION

Probabilistic aspects of “computer analogy” method for solving differential equations

V. V. Aristov^a, A. V. Stroganov<sup>b

a</sup> Dorodnicyn Computing Center of the RAS, CC RAS, Vavilov str. 40, Moscow, 119333, Russia
^b Moscow State Institute of Radioengineering, Electronics and Automation (Technical University), Vernadskogo av. 78, Moscow, 119454, Russia

Abstract: Method which allows to obtain explicit form of the solution as a part of power series of the argument step is developed. Formalization of characteristics of the algorithm analogous to operations of a computer is performed. The operation of transfer from one rank to another leads to a probability scheme of the algorithm that averages unknown intermediate steps in higher ranks of the series. The stochastic characteristics of the method are studied and illustrated. Examples of solving nonlinear equations and systems of nonlinear differential equations are presented.

Keywords: “computer analogy” method, differential equations solving, Cauchy problem.

Received: 27.03.2008

DOI: 10.20537/2076-7633-2009-1-1-21-31