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

Figure 6

(a) Comparison of the approximations for the standard deviation 𝜎[𝑋(𝑡)] on the time-interval 𝑡∈[0,2] in Example 4 by using Fröbenius and Polynomial Chaos. We assume that 𝜂=(𝐴,𝑌₀,𝑌₁)^⊤ follows a multivariate Gaussian distribution: 𝜂∼𝑁(𝝁_𝜂;𝚺_𝜂) where 𝝁_𝜂=(−2,3,6)^⊤ and 𝚺¹_𝜂 and 𝚺²_𝜂 are given by (35) corresponding to statistical independence and dependence, respectively. (b) Difference between the approximations showed in the figure on (a).

(a)

(b)