Evelyn Buckwar, Pedro Lima,
"Computational Methods for Two-Dimensional Neural Fields"
, in L.A. Uvarova,A.B. Nadykto, A.V. Latyshev: Nonlinearity: Problems, Solutions and Applications, Nova Science Publishers,, New York, 2017
Computational Methods for Two-Dimensional Neural Fields
Sprache des Titels:
Nonlinearity: Problems, Solutions and Applications
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.