Database of the illustrative simulations of the nonstandard approximation of the generalized Burgers–Huxley equation

The presented dataset is a result of numerical analysis of a generalized Burgers–Huxley partial differential equation. An analyzed diffusive partial differential equation consist with nonlinear advection and reaction. The reaction term is a generalized form of the reaction law of the Hodgkin–Huxley model, while the advection is a generalized form of the corresponding term in the classical Burgers equation. This generalized Burgers–Huxley equation possesses travelling-wave solutions that are positive and bounded. Moreover, such solutions are spatially monotone at each instant of time, and temporally monotone at each spatial point. Unfortunately, only a few travelling-wave solutions of such model are known in exact form, therefore, the construction of a suitable numerical method is highly desirable.