  We are concerned with the numerical solution of a class integro-differential
equations, known as Neural Field Equations, which describe the large-scale
dynamics of spatially structured networks of neurons. These equations have many
applications in Neuroscience and Robotics. We describe a numerical method for
the approximation of solutions in the two-dimensional case, including a
space-dependent delay in the integrand function. Compared with known algorithms
for this type of equation we propose a scheme with higher accuracy in the time
discretisation. Since computational efficiency is a key issue in this type of
calculations, we use a new method for reducing the complexity of the algorithm.
The convergence issues are discussed in detail and a number of numerical
examples is presented, which illustrate the performance of the method.
