| Zugriffsnummer | 45211 |
| Dokumenttyp | Zeitschriftenartikel |
| Peer Review | mit Peer Review |
| Sprache | Englisch |
| Titel | A splitting/polynomial chaos expansion approach for stochastic evolution equations |
| Autor(in); Institution |
Kofler, Andreas; 8.1, Biomedizinische Magnetresonanz, PTB-Berlin
Levajkovic, Tijana; Institute of Stochastics and Business Mathematics, Vienna University of Technology, Vienna, AUSTRIA
Mena, Hermann; Department of Mathematics, Yachay Tech University, Urcuquí, ECUADOR
Ostermann, Alexander; Department of Mathematics, University of Innsbruck, Innsbruck, AUSTRIA
|
| Quelle/Jahr | Journal of Evolution Equations: 21 (2021), 2, 1345 - 1381 |
| ISSN | 1424-3199 (PRINT) ; 1424-3202 (ONLINE) |
| DOI | |
| Verlag | Berlin: Springer |
| Klassifikationscode | MSC: 60H35 ; MSC: 65M75 ; MSC: 65J10 ; MSC: 60H40 ; MSC: 65M12 ; MSC: 11B83 |
| Freie Schlagworte | Splitting methods ; Analytic semigroups ; Resolvent splitting ; Polynomial chaos expansion ; Fourier–Legendre polynomials ; Wiener–Legendre expansion |
| Zusammenfassung | In this paper, we combine deterministic splitting methods with a polynomial chaos expansion method for solving stochastic parabolic evolution problems. The stochastic differential equation is reduced to a system of deterministic equations that we solve efficiently by splitting methods. The method can be applied to a wide class of problems where the related stochastic processes are given uniquely in terms of stochastic polynomials. A comprehensive convergence analysis is provided and numerical experiments validate our approach. |
| Themenbereich der Metrologie | Metrologie in der Medizin |