Abstract
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.
| Original language | English |
|---|---|
| Title of host publication | Nonlinearity: Problems, Solutions and Applications |
| Editors | L.A. Uvarova,A.B. Nadykto, A.V. Latyshev |
| Place of Publication | New York |
| Publisher | Nova Science Publishers, |
| Number of pages | 29 |
| Publication status | Published - 2017 |
Fields of science
- 101 Mathematics
- 101014 Numerical mathematics
- 101018 Statistics
- 101019 Stochastics
- 101024 Probability theory
JKU Focus areas
- Computation in Informatics and Mathematics
- Engineering and Natural Sciences (in general)