In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media. Two types of models are presented: The first has a time-dependent coefficient modeled by the Ornstein–Uhlenbeck process. The second has a random field coefficient with a given covariance in space. For the former a formula for the exact solution in terms of moments is derived. In both cases stable numerical schemes are introduced to solve these random partial differential equations. Simulation results including convergence studies conclude the theoretical findings.
%0 Journal Article
%1 barth2017uncertainty
%A Barth, Andrea
%A Fuchs, Franz G.
%D 2017
%I Elsevier
%J Applied numerical mathematics
%K exc310 ians ians-uq myown
%P 38-51
%R 10.1016/j.apnum.2017.06.009
%T Uncertainty quantification for linear hyperbolic equations with stochastic process or random field coefficients
%U https://doi.org/10.1016/j.apnum.2017.06.009
%V 121
%X In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media. Two types of models are presented: The first has a time-dependent coefficient modeled by the Ornstein–Uhlenbeck process. The second has a random field coefficient with a given covariance in space. For the former a formula for the exact solution in terms of moments is derived. In both cases stable numerical schemes are introduced to solve these random partial differential equations. Simulation results including convergence studies conclude the theoretical findings.
@article{barth2017uncertainty,
abstract = {In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media. Two types of models are presented: The first has a time-dependent coefficient modeled by the Ornstein–Uhlenbeck process. The second has a random field coefficient with a given covariance in space. For the former a formula for the exact solution in terms of moments is derived. In both cases stable numerical schemes are introduced to solve these random partial differential equations. Simulation results including convergence studies conclude the theoretical findings.},
added-at = {2023-12-01T15:36:15.000+0100},
affiliation = {Barth, A (Reprint Author), Univ Stuttgart, SimTech, Pfaffenwaldring 5a, D-70569 Stuttgart, Germany.
Barth, Andrea, Univ Stuttgart, SimTech, Pfaffenwaldring 5a, D-70569 Stuttgart, Germany.
Fuchs, Franz G., Sintef ICT, Forskningsveien 1, N-0314 Oslo, Norway.},
author = {Barth, Andrea and Fuchs, Franz G.},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2181d0f254008c73ecb229c875cb11e3e/abarth},
doi = {10.1016/j.apnum.2017.06.009},
interhash = {0d4796c28d82856fcbf8fcfa489c196d},
intrahash = {181d0f254008c73ecb229c875cb11e3e},
issn = {{1873-5460} and {0168-9274}},
journal = {Applied numerical mathematics},
keywords = {exc310 ians ians-uq myown},
language = {eng},
month = {November},
pages = {38-51},
publisher = {Elsevier},
research-areas = {Mathematics},
timestamp = {2023-12-04T12:47:25.000+0100},
title = {Uncertainty quantification for linear hyperbolic equations with stochastic process or random field coefficients},
unique-id = {ISI:000410013800003},
url = {https://doi.org/10.1016/j.apnum.2017.06.009},
volume = 121,
year = 2017
}
