dc.contributor.author |
Garba, Salisu M.
|
|
dc.contributor.author |
Gumel, Abba B.
|
|
dc.contributor.author |
Hassan, Adamu Shitu
|
|
dc.contributor.author |
Lubuma, Jean M.-S.
|
|
dc.date.accessioned |
2015-03-24T09:09:36Z |
|
dc.date.available |
2015-03-24T09:09:36Z |
|
dc.date.issued |
2015-05 |
|
dc.description.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. |
en_ZA |
dc.description.librarian |
hb2015 |
en_ZA |
dc.description.sponsorship |
Three of the authors (SMG, ASH and JM-SL) acknowledge the support of the South African DST/NRF
SARChI chair in Mathematical Models and Methods in Bioengineering and Biosciences (M3B2). ASH
acknowledges the support of MacArthur Foundation, Bayero University, Kano, Nigeria. ABG acknowledges,
with thanks, the support, in part, of the Natural Science and Engineering Research Council
(NSERC) of Canada. |
en_ZA |
dc.description.uri |
http://www.elsevier.com/ locate/amc |
en_ZA |
dc.identifier.citation |
Garba, 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. |
en_ZA |
dc.identifier.issn |
0096-3003 (print) |
|
dc.identifier.issn |
1873-5649 (online) |
|
dc.identifier.other |
10.1016/j.amc.2015.01.088 |
|
dc.identifier.uri |
http://hdl.handle.net/2263/44130 |
|
dc.language.iso |
en |
en_ZA |
dc.publisher |
Elsevier |
en_ZA |
dc.rights |
© 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. |
en_ZA |
dc.subject |
Delay differential equations |
en_ZA |
dc.subject |
Exact scheme |
en_ZA |
dc.subject |
Dynamic stability |
en_ZA |
dc.subject |
Nonstandard finite difference (NSFD) scheme |
en_ZA |
dc.title |
Switching from exact scheme to nonstandard finite difference scheme for linear delay differential equation |
en_ZA |
dc.type |
Postprint Article |
en_ZA |