الفهرس 
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Abstract
We study one of the developed techniques for solving a class of stochastic nonlinear differential equations (SNDEs). This technique is called the Wiener-Chaos expansion technique (WCE). The application of this technique results in a system of deterministic differential equations (DDEs). The resulting DDEs are solved by deterministic numerical techniques, which is suitable for the conditions of the original equations. By solving these DDEs, we can get the statistical properties of the solution using simple formulas. Therefore, we introduce some theoretical results that help us in our study. Comparing the results of the WCE with the results of both the Winere-Hermite expansion (WHE) and the Monte Carlo simulations, we conclude that the concerned technique is more accurate, efficient, easy and programmable compared with the other techniques. Therefore, we use the WCE technique to solve many SNDEs either stochastic ordinary differential equations (SODEs) or stochastic partial differential equations (SPDEs), under the influence of either additive random forcing or multiplicative random forcing. Some of these equations are considered as a challenge for studying the behavior of its solutions. The difficulty is due to the strength of the nonlinear terms in these equations, such as Van der pol equation and Duffing Van der Pol equation. Hence, we introduce a formula that helps to handle the nonlinear terms of the stochastic differential equations. The agreement between the results of the WCE, WHE, and Monte Carlo techniques reflects the validity of the closed-form of the developed analytical formula for the product of more than two Wiener Chaos expansions.