Numerical Method for Neural Field Models with Transmission Delays
DescriptionBased on the recent development in meshless local radial basis functions for numerical approximation of stiff partial differential equations, we attempt to develop in this proposed project an efficient and effective numerical algorithm for solving neural field models with transmission delays formulated as integro-differential equations. This can be achieved by coupling the localized radial basis functions-based pseudo-special method with the exponential time differencing scheme to provide an accurate approximation of the solutions of the neural field models under both uniform and non-uniform discretizations. This combined approach inherits the meshless and highly accurate advantages of these two methods in spatial and temporal approximations. The primary advantage of the meshless local radial basis function-based pseudo-spectral method (LRBF-PSM), lies in its potential for approximating high dimensional problems under irregular boundaries using scattered collocation points. The idea of LRBF-PSM is based on the construction of a set of orthogonal functions by meshless radial basis functions (RBFs) on each overlapping sub-domain. With the meshless advantage of LRBF, the pseudo-spectral method can easily be extended to solve multi-dimensional problems under irregular domains. Specifically, we will approximate the time variable using both implicit-explicit (IMEX) and time-splitting (TS) schemes. The computational efficiency of the numerical algorithm will further be improved by combining the meshless computational methods with techniques of adaptive point allocation and unconditional stable integration schemes.
|Effective start/end date||1/09/21 → …|