numerical solution of second-order stochastic dierential equations with gaussian random parameters

in this paper, we present the numerical solution of ordinary dierential equations (or sdes), from each order especially second-order with time-varying and gaussian random coecients. we indicate a complete analysis for second-order equations in special case of scalar linear second-order equations (damped harmonic oscillators with additive or multi- plicative noises). making stochastic dierential equations system from this equation, it could be approximated or solved numerically by dierent numerical methods. in the case of linear stochastic dierential equations system by computing fundamental matrix of this system, it could be calculated based on the exact solution of this system. finally, this stochastic equa- tion is solved by numerically method like euler-maruyama and milstein. also its asymptotic stability and statistical concepts like expectation and variance of solutions are discussed.