Evelyn Buckwar, Pedro Lima,
"Numerical solution of the neural field equation in the two-dimensional case"
, in SIAM Journal on Scientific Computing, Vol. 37, Nummer 6, Society for Industrial and Applied Mathematics, Seite(n) B962?B979, 2015, ISSN: 1064-8275
Numerical solution of the neural field equation in the two-dimensional case
Sprache des Titels:
We are concerned with the numerical solution of a class of 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 discretization. Since computational efficiency is a key issue in this type of calculation, 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 are presented, which illustrate the performance of the method.
Read More: http://epubs.siam.org/doi/abs/10.1137/15M1022562?journalCode=sjoce3