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The exponential integrator scheme for stochastic partial differential equations: Pathwise error bounds

2010; Elsevier BV; Volume: 235; Issue: 5 Linguagem: Inglês

10.1016/j.cam.2010.08.011

1879-1778

Peter E. Kloeden, Gabriel J. Lord, Andreas Neuenkirch, Tony Shardlow,

Numerical methods for differential equations

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).