Journal:Applied Numerical Mathematics
Key Words:Stochastic partial differential equations; Invariant measure; Ergodicity; Weak approximation; Exponential Euler scheme
Abstract:We discrete the ergodic semilinear stochastic partial differential equations in space dimension d ≤3with additive noise, spatially by a spectral Galerkin method and temporally by an exponential Euler scheme. It is shown that both the spatial semi-discretization and the spatio-temporal full discretization are ergodic. Further, convergence orders of the numerical invariant measures, depending on the regularity of noise, are recovered based on an easy time-independent weak error analysis without relying on Malliavin calculus. To be precise, the convergence order is 1-epsilon in space and 1/2-epsilon in time for the space-time white noise case and 2 -epsilon in space and 1-epsilon in time for the trace class noise case in space dimension d =1, with arbitrarily small epsilon>0. Numerical results are finally reported to confirm these theoretical findings.
Co-author:Chen Ziheng, Gan Siqing, Wang Xiaojie
Indexed by:Journal paper
Document Type:J
Volume:157
Page Number:135–158
Translation or Not:no
Included Journals:SCI