Abstract Summation-by-parts (SBP) operators have a number of properties that make them
an attractive option for higher-order spatial discretizations of partial differential equations. In …

High-order finite difference methods are efficient, easy to program, scale well in multiple
dimensions and can be modified locally for various reasons (such as shock treatment for …

For the response analysis of the structural–acoustic system without sufficient information, an
interval random model is introduced. In the interval random model, the uncertain parameters …

We consider a hyperbolic system with uncertainty in the boundary and initial data. Our aim is
to show that different boundary conditions give different convergence rates of the variance of …

The acoustic field with convex parameters widely exists in the engineering practice. The
vertex method and the anti-optimization method are not considered as appropriated …

We present a well-posed stochastic Galerkin formulation of the incompressible Navier–
Stokes equations with uncertainty in model parameters or the initial and boundary …

We present a local sensitivity analysis for the hydrodynamic Cucker-Smale (HCS) model
with random inputs. In the absence of random inputs, the HCS model was derived as a …

This paper concerns accurate and efficient polynomial chaos expansions (PCEs) for Asian
option pricing with uncertain volatilities. While arbitrary distributions of the volatility …

In this thesis, we introduce random elements into the Cucker-Smale (CS) model and provide
quantitative analyses for those uncertainties. In real applications of the Cucker-Smale …

This chapter aims to present accurate and stable numerical schemes for the solution of a
class of linear diffusive transport problems. The advection-diffusion equation subject to …