Numerical approximation of a convolution model of ˙ θ-neuron networks

Abstract

In this article, we consider a nonlinear integro-differential equation that arises in a ˙ θ-neural networks modeling. We analyze boundedness and invertibility of the model operator, construct approximate solutions using piecewise polynomials in space, and estimate the theoretical convergence rate of such spatial approximations. We present some numerical experimental results to demonstrate the scheme.