Two boundedness and monotonicity preserving methods for a generalized Fisher-KPP equation

Conditional full stability of positivity-preserving finite difference scheme for diffusion–advection-reaction models

“…The relative error at t = 1 for the numerical solution by the proposed ETD method in Example 1.a) is presented in Table 2. Results demonstrate competitive accuracy with respect to the semi-explicit finite difference methods proposed in [23].…”

“…where the unknown u in [22], initial and boundary conditions are defined by a family of the travelling wave solutions with the arbitrary real numbers φ and C given in [23]. Table 1 for the cases a) and b) correspondingly, as it is proposed in [23]. The relative error at t = 1 for the numerical solution by the proposed ETD method in Example 1.a) is presented in Table 2.…”

Numerical Methods for Multidisciplinary Free Boundary Problems: Numerical Analysis and Computing

“…under the crucial restriction that in the previous papers the spatial domain is not constrained by the population behavior, that is the essence of the Stefan condition. The first diffusive logistic model related to biological invasions was initiated in 1937, of course without boundary restric-POPULATION DYNAMICS OF AN INVASIVE SPECIES on the stability and the preservation of the qualitative properties of the theoretical solution[11,52,63].To our knowledge the seminal paper[30] by Du and Lin is the first contribution in the field of spreading of populations where a Stefan condition is used and man-…”