Abstract:
One-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.
