Effective Numerical Solution to Two-Dimensional Stochastic Neural Field Equations

Abstract

In this paper, we explore an efficient numerical integration scheme for solving 2D Neural Field Equations(NFEs) in the presence of external stimuli input in both deterministic and stochastic scenarios. The method is based on Galerkin-type spectral approximation and our attention is paid to its efficient implementation because of the partial integro-differential fashion of the NFEs under discussion and two-dimensional spatial domain. The straightforward implementation of the proposed numerical scheme yields a very time consuming method in case of a good spatial resolution. Our efforts are focused on translating the numerical technique into a high-level computer code in MATLAB where the improved efficiency is achieved by vectorizing operations and accessing subarrays via MATLAB’s colon notation. The results of numerical experiments are presented.