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We are concerned with the numerical solution of a class integro-differentialequations, known as Neural Field Equations, which describe the large-scaledynamics of spatially structured networks of neurons. These equations have manyapplications in Neuroscience and Robotics. We describe a numerical method forthe approximation of solutions in the two-dimensional case, including aspace-dependent delay in the integrand function. Compared with known algorithmsfor this type of equation we propose a scheme with higher accuracy in the timediscretisation. Since computational efficiency is a key issue in this type ofcalculations, we use a new method for reducing the complexity of the algorithm.The convergence issues are discussed in detail and a number of numericalexamples is presented, which illustrate the performance of the method.

Numerical Solution of the Neural Field Equation in the Two-dimensional Case