Boundary procedures for the time-dependent Burgers' equation under uncertainty

P Pettersson, J Nordström, G Iaccarino - Acta Mathematica Scientia, 2010 - Elsevier
The Burgers' equation with uncertain initial and boundary conditions is approximated using
a Polynomial Chaos Expansion (PCE) approach where the solution is represented as a
series of stochastic, orthogonal polynomials. The resulting truncated PCE system is solved
using a novel numerical discretization method based on spatial derivative operators
satisfying the summation by parts property and weak boundary conditions to ensure stability.
The resulting PCE solution yields an accurate quantitative description of the stochastic …
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