@MASTERSTHESIS\{IMM2013-06664,
    author       = "E. K. Nielsen",
    title        = "Study in Modern Uncertainty Quantification Methods",
    year         = "2013",
    school       = "Technical University of Denmark, Department of Applied Mathematics and Computer Science / {DTU} Co",
    address      = "Matematiktorvet, Building 303B, {DK-}2800 Kgs. Lyngby, Denmark, compute@compute.dtu.dk",
    type         = "",
    note         = "{DTU} supervisor: Allan P. Engsig-Karup, apek@dtu.dk, {DTU} Compute",
    url          = "http://www.compute.dtu.dk/English.aspx",
    abstract     = "Uncertainty Quantification (UQ) is a relatively new research area where there over the past years have been an ongoing development in techniques to improve the existing {UQ} methods. As the demand on quantifying uncertainties are increasing the methods becomes more widely used. The goal with the thesis is to apply {UQ} using generalized Polynomial Chaos (gPC) expansion together with spectral numerical methods on differential equation. Furthermore experiences with the programming language Python must be gained in order to implement the {UQ} methods.
The thesis starts by introducing the mathematical background of the spectral method including e.g. orthogonal polynomials and quadrature rules. Three differently {UQ} methods is, after the introduction of gPC, presented.
To illustrate uncertainty, the {UQ} method are applied on two stochastic differential equations showing the beneficial by using spectral methods illustrated by the spectral convergence.
The final part dealing with the illustration of the curse of dimensionality. It also contains 1 technique handling the dimensionality which is satisfied to some extend."
}