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

Kloeden, P. E.; Shott, S.

doi:https://doi.org/10.1155/S1048953301000053

International Journal of Stochastic Analysis

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Volume 14 |Article ID 697341 | https://doi.org/10.1155/S1048953301000053

P. E. Kloeden, S. Shott, "Linear-implicit strong schemes for Itô-Galkerin approximations of stochastic PDEs", International Journal of Stochastic Analysis, vol. 14, Article ID 697341, 7 pages, 2001. https://doi.org/10.1155/S1048953301000053

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

P. E. Kloeden

¹ and S. Shott²

¹Johann Wolfgang Goethe Universität,, Fachbereich Mathematik, Germany

²University of Tasmania, Department of Mathematics, Hobart, Australia

Received01 Aug 1999

Revised01 Dec 1999

Abstract

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 γ strong linear-implicit Taylor scheme with time-step Δ 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 λ1≤λ2≤… in its drift term is then estimated by K(λN+1−½+Δγ) 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.

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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.

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