Garba, Salisu M.Gumel, Abba B.Hassan, Adamu ShituLubuma, Jean M.-S.2015-03-242015-03-242015-05Garba, SM, Gumel, AB, Hassan, AS & Lubuma, JMS 2015, 'Switching from exact scheme to nonstandard finite difference scheme for linear delay differential equation', Applied Mathematics and Computation, vol. 258, pp.388-403.0096-3003 (print)1873-5649 (online)10.1016/j.amc.2015.01.088http://hdl.handle.net/2263/44130One-dimensional models are important for developing, demonstrating and testing new methods and approaches, which can be extended to more complex systems. We design for a linear delay differential equation a reliable numerical method, which consists of two time splits as follows: (a) It is an exact scheme at the early time evolution −τ ≤ t ≤ τ, where τ is the discrete value of the delay; (b) Thereafter, it is a nonstandard finite difference (NSFD) scheme obtained by suitable discretizations at the backtrack points. It is shown theoretically and computationally that the NSFD scheme is dynamically consistent with respect to the asymptotic stability of the trivial equilibrium solution of the continuous model. Extension of the NSFD to nonlinear epidemiological models and its good performance are tested on a numerical example.en© 2015 Elsevier Inc. All rights reserved. Notice : this is the author’s version of a work that was accepted for publication in Applied Mathematics and Computation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied Mathematics and Computation, vol. 258, pp. 388-403, 2015. doi : 10.1016/j.amc.2015.01.088.Delay differential equationsExact schemeDynamic stabilityNonstandard finite difference (NSFD) schemePostprint Article