Time‐Dependent Polynomial Chaos | Zendy

Marc Gerritsma | Zendy; Peter Vos | Zendy; JanBart van der Steen | Zendy

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Time‐Dependent Polynomial Chaos

Author(s) -

Marc Gerritsma,

Peter Vos,

JanBart van der Steen

Publication year - 2008

Publication title -

aip conference proceedings

Language(s) - English

Resource type - Conference proceedings

SCImago Journal Rank - 0.177

H-Index - 75

eISSN - 1551-7616

pISSN - 0094-243X

DOI - 10.1063/1.2990897

Subject(s) - polynomial chaos , convergence (economics) , polynomial , mathematics , probability density function , monte carlo method , constant (computer programming) , function (biology) , chaos (operating system) , computer science , mathematical analysis , statistics , computer security , evolutionary biology , economics , biology , programming language , economic growth

Conventional generalized polynomial chaos is known to fail for long time integration, loosing its optimal convergence behaviour and developing unacceptable error levels. The reason for this loss of convergence is the assumption that the probability density function is constant in time. By allowing a probability density function to evolve in time the optimal properties of polynomial chaos are retrieved without resorting to high polynomial degrees.This time‐dependent approach is applied to a system of coupled non‐linear differential equations. These results are compared to the conventional generalized polynomial chaos solutions and Monte Carlo simulations.

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