Nonstandard discretizations of the generalized Nagumo reaction-diffusion equation

A competitive nonstandard semi-explicit finite-difference method is constructed and used to obtain numerical solutions of the diffusion-free generalized Nagumo equation. Qualitative stability analysis and numerical simulations show that this scheme is more robust in comparison to some standard explicit methods such as forward Euler and the fourth-order Runge-Kutta method (RK4). The nonstandard scheme is extended to construct a semi-explicit and an implicit scheme to solve the full Nagumo reaction-diffusion equation.