A method based on the meshless approach for the numerical solution of the singularly perturbed differential-difference equation arising in the modeling of neuronal variability

Akhavan Ghassabzade, Fahimeh; Saberi-Nadjafi, Jafar; Soheili, Ali Reza

doi:10.22080/cjms.2020.18475.1474

A method based on the meshless approach for the numerical solution of the singularly perturbed differential-difference equation arising in the modeling of neuronal variability

Document Type : Research Articles

Authors

¹ Department of Mathematics, Faculty of Sciences, University of Gonabad, Gonabad, Iran.

² Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran.

³ Department of Applied Mathematics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran. Mashhad&lrm;, &lrm;Iran.

10.22080/cjms.2020.18475.1474

Abstract

In this paper, an efficient procedure based on the multiquadric radial
basis functions (RBFs) collocation method is applied for the numerical so-
lution of the singularly perturbed differential-difference (SPDDE) equation.
The method is coupled with the Residual subsampling algorithm for sup-
port adaptivity. The problem considered in this paper shows turning point
behavior which is added to the complexity in the construction of numerical
approximation to the solution of the problem. The proposed algorithm is
very simple to perform. Some numerical examples are given to validate the
computational efficacy of the suggested numerical scheme.

Keywords