Exponentially fitted methods on layer-adapted mesh for singularly perturbed delay differential equations

Erdogan, Fevzi2018-04-112018-04-112016Erdogan F. Exponentially fitted methods on layer-adapted mesh for singularly perturbed delay differential equations / Fevzi Erdogan // Litteris et Artibus : proceedings of the 6th International youth science forum, November 24–26, 2016, Lviv, Ukraine / Lviv Polytechnic National University. – Lviv : Lviv Polytechnic Publishing House, 2016. – P. 91–92. – Bibliography: 20 titles.https://ena.lpnu.ua/handle/ntb/40260The purpose of this study is to present a uniform finite difference method for numerical solution of a initial value problem for quasi-linear second order singularly perturbed delay differential equation. A numerical method is constructed for this problem which involves appropriate piecewise-uniform Shishkin mesh on each time subinterval. The method is shown to uniformly convergent with respect to the perturbation parameter. A numerical experiment illustrate in practice the result of convergence proved theoretically.enThe finite difference methodAppropriate piecewise-uniform Shishkin meshExponentially fitted methods on layer-adapted mesh for singularly perturbed delay differential equationsConference Abstract91-92