dc.contributor.author |
Aderogba, Adebayo Abiodun
|
|
dc.contributor.author |
Chapwanya, Michael
|
|
dc.date.accessioned |
2016-02-09T12:40:48Z |
|
dc.date.issued |
2015-07 |
|
dc.description.abstract |
We design explicit nonstandard finite difference schemes for the nonlinear Allen-Cahn reaction
diffusion equation in the limit of very small interaction length ". In the proposed scheme, the
perturbation parameter is part of the argument of the functional step size, thereby minimis-
ing the restrictions normally associated with standard explicit finite difference schemes. The
derivation involves splitting the equation into the space independent and the time independent
different models. An exact nonstandard scheme is proposed for the space independent model
and energy conservative schemes are proposed for the time independent model. We show the
power of the derived scheme over the existing schemes through several numerical examples. |
en_ZA |
dc.description.embargo |
2016-07-31 |
|
dc.description.librarian |
hb2015 |
en_ZA |
dc.description.sponsorship |
South African DST/NRF SARChI Chair on Mathematical Models and Methods in Bioengineering and Biosciences (M3B2). |
en_ZA |
dc.description.uri |
http://www.tandfonline.com/loi/gdea20 |
en_ZA |
dc.identifier.citation |
A.A. Aderogba & M. Chapwanya (2015) An explicit nonstandard finite difference scheme for the Allen–Cahn equation, Journal of Difference Equations and Applications, 21:10, 875-886, DOI: 10.1080/10236198.2015.1055737. |
en_ZA |
dc.identifier.issn |
1023-6198 (print) |
|
dc.identifier.issn |
1563-5120 (online) |
|
dc.identifier.other |
10.1080/10236198.2015.1055737 |
|
dc.identifier.uri |
http://hdl.handle.net/2263/51293 |
|
dc.language.iso |
en |
en_ZA |
dc.publisher |
Taylor and Francis |
en_ZA |
dc.rights |
© 2015 Taylor and Francis. This is an electronic version of an article published in Journal of Difference Equations and Applications, vol. 21, no.10, pp. 875-886, 2015, doi :10.1080/10236198.2015.1055737. Journal of Difference Equations and Applications is available online at : http://www.tandfonline.comloi/gdea20. |
en_ZA |
dc.subject |
Allen-Cahn equation |
en_ZA |
dc.subject |
Nonstandard finite difference |
en_ZA |
dc.subject |
Explicit scheme |
en_ZA |
dc.title |
An explicit nonstandard finite difference scheme for the Allen-Cahn equation |
en_ZA |
dc.type |
Postprint Article |
en_ZA |