On the Transient Solution of Non-Deterministic Systems

Through the use of formal expansions, a non-deterministic solution approach is developed for systems modeled by first order matrix differential equations with random coefficients and input conditions. The generality of the solution procedure is such that various statistical moments can be generated. In particular, this includes such moments as the mean and standard deviation vectors, the variance-covariance matrix etc. To ascertain the overall properties of such moments, various recursive generators as well as convergence and truncation criteria are developed. Due to the formal structure of the overall solution, the inherent algorithmic apparatus is concise and easily programmed. Because of this, the procedure can be applied equally well to both large and small systems of non-deterministic modeling equations. A further feature of the given procedure lies in the fact that it can be used to generate the statistical solution for a given element of the dependent variable vector without necessitating the development of the entire solution. To demonstrate the scope of the approach, several numerical experiments are included in the paper.