Numerical Solution of the Neural Field Equation in the Two-dimensional Case
This work provides an improved numerical solver for neural field equations, which are important for modeling large-scale neural dynamics in neuroscience and robotics.
The paper presents a numerical method for solving two-dimensional neural field equations with space-dependent delays, achieving higher accuracy in time discretization and improved computational efficiency through a complexity-reduction technique.
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.