A hybrid numerical scheme for singularly perturbed parabolic differential‐difference equations arising in the modeling of neuronal variability. Issue 5 (8th July 2021)

• Record Type: Journal Article
• Authors: Takele Daba, Imiru; File Duressa, Gemechis
• Is Part Of: Computational and mathematical methods. Volume 3:Issue 5(2021)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2021-07-08
• Subjects: delay differential equations -- hybrid numerical scheme -- singular perturbation; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Periodicals; Numerical analysis; Mathematics -- Data processing; Periodicals; 004.0151
• DOI: 10.1002/cmm4.1178
• Languages: English
• ISSNs: 2577-7408

Abstract

Abstract: This study aims at constructing a robust numerical scheme for solving singularly perturbed parabolic delay differential equations arising in the modeling of neuronal variability. Taylor's series expansion is applied to approximate the shift terms. The obtained result is approximated by using the implicit Euler method in the temporal discretization on a uniform step size with the hybrid numerical scheme consisting of the midpoint upwind method in the outer layer region and the cubic spline in tension method in the inner layer region on a piecewise uniform Shishkin mesh in the spatial discretization. The constructed scheme is shown to be an ε ‐uniformly convergent accuracy of order O Λ t + N − 2 ln 3 N . Two model examples are given to testify the theoretical findings.