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Zbl 1015.65036
Mickens, Ronald E.
A nonstandard finite difference scheme for the diffusionless Burgers equation with logistic reaction. (English)
[J] Math. Comput. Simul. 62, No.1-2, 117-124 (2003). ISSN 0378-4754

Summary: 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.

MSC 2000:: *65M06 Finite difference methods (IVP of PDE)
35Q53 KdV-like equations

Keywords: Burgers equation; nonstandard finite difference schemes; nonlinear logistic reaction term; numerical examples

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