Numerical solution of random ordinary differential equations by using modified decomposition method

In the following work, we employ the modified decomposition method to obtain approximate solutions to random ordinary linear and nonlinear differential equations. We will introduce a fast technique for finding approximate solutions and demonstrate the effectiveness, speed, and accuracy of this method through examples, the obtained results, and the impact of the stochastic process (generation of a Wiener process on a computer) on the shape of the solution to differential equations.