Maximum Principles for Discrete and Semidiscrete Reaction-Diffusion Equation

Figure 4

Bounds of solutions of the discrete Nagumo equation (78) with and and their dependence on the values of and (a) and on the values of space and time discretization steps and for a fixed (b). In the light gray area, the bounds follow from Theorem 9. In the dark gray area, the bounds are implied by Theorem 11 and is given by (81). In the white area we have no bounds on solutions.

(a)

(b)