TY - JOUR
T1 - The exponential integrator scheme for stochastic partial differential equations
T2 - Pathwise error bounds
AU - Kloeden, P. E.
AU - Lord, G. J.
AU - Neuenkirch, A.
AU - Shardlow, T.
PY - 2011/1/1
Y1 - 2011/1/1
N2 - We present an error analysis for the pathwise approximation of a general semilinear stochastic evolution equation in d dimensions. We discretise in space by a Galerkin method and in time by using a stochastic exponential integrator. We show that for spatially regular (smooth) noise the number of nodes needed for the noise can be reduced and that the rate of convergence degrades as the regularity of the noise reduces (and the noise becomes rougher). © 2010 Elsevier B.V. All rights reserved.
AB - We present an error analysis for the pathwise approximation of a general semilinear stochastic evolution equation in d dimensions. We discretise in space by a Galerkin method and in time by using a stochastic exponential integrator. We show that for spatially regular (smooth) noise the number of nodes needed for the noise can be reduced and that the rate of convergence degrades as the regularity of the noise reduces (and the noise becomes rougher). © 2010 Elsevier B.V. All rights reserved.
KW - Galerkin method
KW - Numerical solution of stochastic PDEs
KW - Pathwise convergence
KW - Stochastic exponential integrator
UR - http://www.scopus.com/inward/record.url?scp=77957873681&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2010.08.011
DO - 10.1016/j.cam.2010.08.011
M3 - Article
SN - 0377-0427
VL - 235
SP - 1245
EP - 1260
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 5
ER -