Two semi-analytical approaches to approximate the solution of stochastic ordinary differential equations with two enormous engineering applications

This study proposes a new large-scale application for efficient semi-analytical techniques, Variation of Parameters Method with an auxiliary parameter and Temimi and Ansari method. In this regard, Variation of Parameters Method with auxiliary parameter and Temimi and Ansari method are advocated to sacrifice an important class of stochastic ordinary differential equations. Two enormous engineering applications with stochastic excitations are solved and compared with the results of the stochastic Runge Kutta method (SRK) to crystallize the accuracy of the proposed methods. Also, a comparison between the two proposed methods is presented. The numerical results demonstrate that Temimi and Ansari method is accurate and readily implemented. It is also worth noting that the proposed two methods have the advantage of easily implantation without linearization or perturbation.