Random analysis of differential equations with homotopy analysis method

In this study, the coefficients or initial conditions of the systems of ordinary, partial and differential equations are chosen from different probability distributions and the equations are randomized. For their random behavior, continuous time probability distributions such as Normal, Gamma, Uniform, Laplace, Beta, and Triangular were examined. These randomized equations are solved by using the concept of homotopy, which is widely used in the solution of non-linear equations in the literature, and the Homotopy Analysis Method, which combines the Taylor series to control the region of convergence and speed of the series solutions. The most commonly used expected value, variance and coefficient of variation from the probability characteristics of the obtained random differential equations were calculated and the graphs of the solutions were drawn with the help of MATLAB or MAPLE package programs.