Abstract
We present and analyze a new space-time nite element method for the solution
of neural eld equations with transmission delays. The numerical treatment of these systems is rare in the literature and currently has several restrictions on the spatial domain and the functionsinvolved, such as connectivity and delay functions. The use of a space-time discretization, with basis functions that are discontinuous in time and continuous in space (dGcG-FEM), is a natural way to deal with space-dependent delays, which is important for many neural eld applications. In
this paper we provide a detailed description of a space-time dGcG-FEM algorithm for neural delay equations, including an a priori error analysis. We demonstrate the application of the dGcG-FEM algorithm on several neural eld models, including problems with an inhomogeneous kernel.
of neural eld equations with transmission delays. The numerical treatment of these systems is rare in the literature and currently has several restrictions on the spatial domain and the functionsinvolved, such as connectivity and delay functions. The use of a space-time discretization, with basis functions that are discontinuous in time and continuous in space (dGcG-FEM), is a natural way to deal with space-dependent delays, which is important for many neural eld applications. In
this paper we provide a detailed description of a space-time dGcG-FEM algorithm for neural delay equations, including an a priori error analysis. We demonstrate the application of the dGcG-FEM algorithm on several neural eld models, including problems with an inhomogeneous kernel.
| Original language | English |
|---|---|
| Pages (from-to) | B797–B818 |
| Journal | SIAM journal on scientific computing |
| Volume | 39 |
| Issue number | 5 |
| DOIs | |
| Publication status | Published - 21 Dec 2017 |
Keywords
- Neural fields
- Transmission delays
- Discontinuous Galerkin finite element methods
- Space-time methods