Analysis of Random Difference Equations Using the Differential Transformation Method

The differential transformation method (DTM) is one of the best methods easily applied to linear and nonlinear difference equations with random coefficients. In this study, we apply the theorems related to the DTM to the given examples and investigate the behaviour of the approximate analytical solutions. The expected value, variance, coefficient of variation, and confidence intervals of the solutions of random difference equations obtained from discrete probability distributions such as uniform, geometric, Poisson, and binomial distributions will be calculated. Maple and MATLAB software packages are used to plot the solution graphs and also to interpret the solution behaviour.