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Convergence of a numerical scheme for SPDEs with correlated noise and global Lipschitz coefficients
Author(s) -
Kamrani Minoo
Publication year - 2016
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3747
Subject(s) - mathematics , stochastic partial differential equation , smoothing , lipschitz continuity , operator (biology) , convergence (economics) , white noise , mathematical analysis , hilbert space , noise (video) , partial differential equation , biochemistry , statistics , chemistry , repressor , artificial intelligence , computer science , transcription factor , economics , image (mathematics) , gene , economic growth
The aim of this paper is to investigate the pathwise numerical solution of semilinear parabolic stochastic partial differential equations (SPDEs) with colored noise instead of the usual space–time white noise. We estimate the numerical solution in the L ∞ topology by a method that takes advantages of the smoothing effect of the dominant linear operator. We consider the case the covariance operator of the forcing does not necessarily commute with the linear operator of the SPDE because of the fact that the Brownian motions are not necessarily independent. We show convergence of this method, and numerical examples give insight into the reliability of the theoretical study. Copyright © 2015 John Wiley & Sons, Ltd.