A Systematic Review on the Solution Methodology of Singularly Perturbed Differential Difference Equations

Gemechis File Duressa (), Imiru Takele Daba and Chernet Tuge Deressa
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Gemechis File Duressa: Department of Mathematics, Jimma University, Jimma P.O. Box 378, Ethiopia
Imiru Takele Daba: Department of Mathematics, Dilla University, Dilla P.O. Box 419, Ethiopia
Chernet Tuge Deressa: Department of Mathematics, Jimma University, Jimma P.O. Box 378, Ethiopia

Mathematics, 2023, vol. 11, issue 5, 1-16

Abstract: This review paper contains computational methods or solution methodologies for singularly perturbed differential difference equations with negative and/or positive shifts in a spatial variable. This survey limits its coverage to singular perturbation equations arising in the modeling of neuronal activity and the methods developed by numerous researchers between 2012 and 2022. The review covered singularly perturbed ordinary delay differential equations with small or large negative shift(s), singularly perturbed ordinary differential–differential equations with mixed shift(s), singularly perturbed delay partial differential equations with small or large negative shift(s) and singularly perturbed partial differential–difference equations of the mixed type. The main aim of this review is to find out what numerical and asymptotic methods were developed in the last ten years to solve such problems. Further, it aims to stimulate researchers to develop new robust methods for solving families of the problems under consideration.

Keywords: singularly perturbed problems; differential–difference equations; systematic review (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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