Linear-implicit strong schemes for Itô-Galkerin approximations of stochastic PDEs

  • Linear-implicit versions of strong Taylor numerical schemes for finite dimensional Itô stochastic differential equations (SDEs) are shown to have the same order as the original scheme. The combined truncation and global discretization error of an gamma strong linear-implicit Taylor scheme with time-step delta applied to the N dimensional Itô-Galerkin SDE for a class of parabolic stochastic partial differential equation (SPDE) with a strongly monotone linear operator with eigenvalues lambda 1 <= lambda 2 <= ... in its drift term is then estimated by K(lambda N -½ + 1 + delta gamma) where the constant K depends on the initial value, bounds on the other coefficients in the SPDE and the length of the time interval under consideration. AMS subject classifications: 35R60, 60H15, 65M15, 65U05.

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Author:Peter E. Kloeden, Stephen Shott
Parent Title (English):Journal of applied mathematics and stochastic analysis
Place of publication:New York, NY
Document Type:Article
Date of Publication (online):2010/09/23
Year of first Publication:2001
Publishing Institution:Universitätsbibliothek Johann Christian Senckenberg
Release Date:2010/09/23
Tag:Galerkin Approximation; Linear-Implicit Scheme; Parabolic SPDE; Strong Taylor Scheme
Page Number:7
First Page:47
Last Page:53
Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Institutes:Informatik und Mathematik / Mathematik
Dewey Decimal Classification:5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik
Licence (German):License LogoCreative Commons - Namensnennung 3.0