A modified semi--implict Euler-Maruyama Scheme for finite element discretization of SPDEs with additive noise

We consider the numerical approximation of a general second order semi--linear parabolic stochastic partial differential equation (SPDE) driven by additive space-time noise. We introduce a new modified scheme using a linear functional of the noise with a semi--implicit Euler--Maruyama method in time and in space we analyse a finite element method (although extension to finite differences or finite volumes would be possible). We prove convergence in the root mean square $L^{2}$ norm for a diffusion reaction equation and diffusion advection reaction equation. We present numerical results for a linear reaction diffusion equation in two dimensions as well as a nonlinear example of two-dimensional stochastic advection diffusion reaction equation. We see from both the analysis and numerics that the proposed scheme has better convergence properties than the standard semi--implicit Euler--Maruyama method

Intraspecific Variation in Taxonomic Characteristics of the Mayfly \u3ci\u3ePotamanthus Myops\u3c/i\u3e (Walsh)

Data collected from an ecological study of the mayfly Potamanthus rnyops (Walsh) in Michigan showed intraspecific variability in taxonomic characteristics that have been employed by previous investigators for species separation. Nymphal dorsal maculation patterns varied considerably within a single population. Also, the ratio of mandibular tusk length to head length increased with successive nymphal instars. Certain adult taxonomic characteristics, particularly relative male imago eye size and distance of separation, were either too poorly defined or too variable to be conclusive in species identification