Random analytic solution of coupled differential models with uncertain initial condition and source term

This paper deals with the construction of random power series solution of vector initial value problems containing uncertainty in both initial condition and source term. Under appropriate hypothesis on the data, we prove that the random series solution constructed by a random Fröbenius method is convergent in the mean square sense. Also, the main statistical functions of the approximating stochastic process solution generated by truncation of the exact series solution are given. Finally, we apply the proposed technique to several illustrative examples.