A nonstandard finite difference scheme for the diffusionless Burgers equation with logistic reaction

Ronald E. Mickens

Mathematics and Computers in Simulation (MATCOM), 2003, vol. 62, issue 1, 117-124

Abstract: A nonstandard finite difference scheme is constructed for the Burgers partial differential equation having no diffusion and a nonlinear logistic reaction term. This scheme preserves the positivity and boundedness properties of the original differential equation and includes the a priori requirement of being semi-explicit. Several other nonstandard discretizations are constructed and their mathematical structures discussed. All of these schemes can be used to calculate numerical solutions for traveling waves problems involving phenomena modeled by the original differential equation.

Keywords: Burgers equation; Nonstandard finite difference schemes; Numerical integration (search for similar items in EconPapers)
Date: 2003
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475402001805
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:62:y:2003:i:1:p:117-124

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().