Dealing with Dependent Uncertainty in Modelling: A Comparative Study Case through the Airy Equation
Table 2
Comparison of the approximations for the standard deviation at different time instants and correlation values in Example 1 by using Fröbenius method with a truncated series with terms (), Polynomial Chaos of order , and Monte Carlo with simulations (). We assume that and the initial condition: follows a bivariate Gaussian distribution: where, according to (25), , , , .