Numerical method for investigation of stability of stochastic integro-differential equations Original Research Article

The present paper is devoted to the numerical solution of the stability problem for linear integro-differential equations, describing the behavior of stochastic viscoelastic systems. The method is based on the statistical simulation of input random wide-band stationary processes and with this aim the method of the canonical expansion is used. For each realization of the process, the numerical solution of integro-differential equations is found. With the help of Liapunov exponents, which are calculated for statistical moments of searched unknowns, the boundaries of the stability with respect to statistical moments of the required order can be obtained. The proposed method allows to investigate the stability of systems excited with stationary processes having the correlation function as well as probability distribution of wide applicability.