**Volume 2, Issue 1, pp 1--7**

**Publication Date**: 2017-12-21

http://dx.doi.org/10.22436/mns.02.01.01

Fevzi Erdogan - Department of Mathematics, Faculty of Sciences, Yuzuncuyil University, 65080, Van, Turkey

Mehmet Giyas Sakar - Department of Mathematics, Faculty of Sciences, Yuzuncuyil University, 65080, Van, Turkey

This study deals with the singularly perturbed initial value problems for a quasilinear first-order delay differential equation. A quasilinearization technique for the appropriate delay differential problem theoretically and experimentally analyzed. The parameter uniform convergence is confirmed by numerical computations.

Delay differential equation, singular perturbation, finite difference scheme, piecewise-uniform mesh, quasilinearization technique

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