An accurate and efficient numerical method for neural field models with transmission delays

Abstract

Based on the recently developed localized radial basis function collocation method (LRBFCM) and exponential time differencing (ETD) method, we derive in this paper an accurate and efficient numerical method for solving neural field models with space-dependent delays formulated as system of integro-differential equations. This combined LRBFCM-ETD method inherits the advantages of these two methods in space and time, thereby offering high accuracy and efficiency for both uniform and non-uniform discretizations, extending the applicability of the method to multi-dimensions easily, and maintaining a good behaviour in a large time-step and long-time integration. Some numerical experiments are presented and numerical results show that the obtained simulations via the LRBFCM-ETD method are reliable and effective for approximating the solution of models investigated in the current paper.