Algorithms of Numerical-spectral Methods for Modeling Stochastic Dynamical Systems

Abstract

Representations of iterated Stratonovich and Ito stochastic integrals are obtained on the basis of the spectral form of mathematical description, they have both theoretical and practical significance. The latter is due to the possibility of constructing quite simple algorithms for the approximate modeling iterated stochastic integrals, which are necessary for the implementation of numerical methods for solving stochastic differential equations. The use of spectral representations of iterated stochastic integrals in numerical methods forms the numerical-spectral methods. Algorithms for them are presented in the form of programs for the computer algebra system Mathcad.