 High order WENO finite volume approximation for population density neuron modelSantosh Kumar and Paramjeet Singh Applied Mathematics and Computation, 2019, vol. 356, issue C, 173-189 Abstract: In this article, we study the excitatory and inhibitory population density model based on leaky integrate-and-fire neuron model. The time evolution of population density is determined by a hyperbolic partial differential equation. There are two factors which might cause difficulties to find the solution. First one is the presence of point-wise delta type source term and second one is the presence of the non-local terms of the voltage of a neuron. We design a high accurate scheme based on WENO-finite volume approximation for spatial discretization. The time evolution is done by SSP-Runge Kutta scheme. To check the efficiency of the designed scheme, we compare the results with the existing scheme in literature. Finally, we remove the non-local terms by diffusion approximation and simulate the model equation. The diffusion approximation is tackled with the Strang splitting method. Some test examples are reported. The performance of the designed scheme is shown by the convergence results. Keywords: Hyperbolic conservation laws; WENO finite volume approximation; Neuronal variability (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:356:y:2019:i:c:p:173-189 DOI: 10.1016/j.amc.2019.03.020 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.