# Numerical Study of Layer Behaviour Differential-Difference Equations With Small Delay Arising in the Nerve Pulse Propagation

## DOI:

https://doi.org/10.26713/cma.v14i1.1970## Keywords:

Singularly perturbed differential-difference equation, Delay, Tridiagonal system, Truncation error## Abstract

In this study, we implement a numerical method to solve a singularly perturbed differential-difference equation with a small shift. Taylor series is used to deal with the small shift, and the given problem converted into a singularly perturbed boundary value problem. To solve this problem, a fourth order finite difference approach is used. The convergence of the method is investigated. The method is supported by the numerical results compared to the other method in the literature. Numerical experiments show how the small shift and perturbation parameter affects the boundary layer solution of the problem.

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*Communications in Mathematics and Applications*,

*14*(1), 385–396. https://doi.org/10.26713/cma.v14i1.1970

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