Dealing with Dependent Uncertainty in Modelling: A Comparative Study Case through the Airy Equation

Figure 3

Comparison of the approximations for the expectation 𝜇[𝑋(𝑡)] on the time-interval 𝑡∈[0,5] in Example 3 by using Fröbenius, Polynomial Chaos, and Monte Carlo simulations. Since the numerical values are indistinguishable graphically, for the sake of clarity in the presentation, nonlabel has been introduced. We assume that 𝜂=(𝐴,𝑌₀,𝑌₁)^⊤ follows a multivariate Gaussian distribution: 𝜂∼𝑁(𝝁_𝜂;𝚺_𝜂) where 𝝁_𝜂=(4,3,6)^⊤ and 𝚺¹_𝜂 and 𝚺²_𝜂 are given by (35) corresponding to statistical independence and dependence, respectively.