TY  - JOUR
A1  - Kloeden, Peter E.
A1  - Shott, Stephen
T1  - Linear-implicit strong schemes for Itô-Galkerin approximations of stochastic PDEs
T2  - Journal of applied mathematics and stochastic analysis
N2  - 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.
KW  - Parabolic SPDE
KW  - Galerkin Approximation
KW  - Strong Taylor Scheme
KW  - Linear-Implicit Scheme
Y1  - 2001
UR  - http://publikationen.ub.uni-frankfurt.de/frontdoor/index/index/docId/8108
UR  - https://nbn-resolving.org/urn:nbn:de:hebis:30-80604
SN  - 1048-9533
N1  - 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.
VL  - 14
IS  - 1
SP  - 47
EP  - 53
PB  - Hindawi
CY  - New York, NY
ER  -