Accuracy Study in Numerical Simulations to Stochastic Neural Field Equations

摘要

This paper elaborates accuracy issues in numerical solutions to Stochastic Neural Field Equations (SNFEs) with the infinite signal transmission speed and in the presence of external stimuli input. The numerical integration method under study belongs to the family of Galerkin-sort spectral approximations of one-dimensional SNFEs considered here. It reduces the partial integro-differential fashion of such models to a large system of ordinary Stochastic Differential Equations (SDEs). Eventually, these SDEs are solved by the Euler-Maruyama scheme of order 0.5 in MATLAB. In this paper, we devise a different-order numerical solution to the SNFE at hand and look at the difference of such stochastic simulations on average for evaluating the consistency of the solution derived. The effect of the SDE-numerical-integration-accuracy on formation of high neuron activity regions (so-called "bumps") is discussed within one SNFE with external stimuli.