Amiraliyev, Gabil M.Erdogan, Fevzi2025-05-102025-05-1020091017-13981572-926510.1007/s11075-009-9306-z2-s2.0-76149127654https://doi.org/10.1007/s11075-009-9306-zhttps://hdl.handle.net/20.500.14720/9810Amiraliyev, Gabil M./0000-0001-6585-7353This study deals with the singularly perturbed initial value problem for a quasilinear first-order delay differential equation. A numerical method is generated on a grid that is constructed adaptively from a knowledge of the exact solution, which involves appropriate piecewise-uniform mesh on each time subinterval. An error analysis shows that the method is first order convergent except for a logarithmic factor, in the discrete maximum norm, independently of the perturbation parameter. The parameter uniform convergence is confirmed by numerical computations.eninfo:eu-repo/semantics/closedAccessDelay Differential EquationSingular PerturbationFinite Difference SchemePiecewise-Uniform MeshError EstimatesArticle524Q1Q1663675WOS:000271736000010