Journal of Applied Mathematics and Stochastic Analysis 
Volume 14 (2001), Issue 1, Pages 47-53
doi:10.1155/S1048953301000053

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

P. E. Kloeden1 and S. Shott2

 1Johann Wolfgang Goethe Universität,, Fachbereich Mathematik, Frankfurt D-60054, Germany
2University of Tasmania, Department of Mathematics, Hobart, Tasmania, Australia
Received 1 August 1999; Revised 1 December 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.