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A nonstandard finite difference scheme for the diffusionless Burgers equation with logistic reaction. (English) Zbl 1015.65036
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:
65M06Finite difference methods (IVP of PDE)
35Q53KdV-like (Korteweg-de Vries) equations