Qualitative Numerical Analysis of a Free-Boundary Diffusive Logistic Model

A two-dimensional free-boundary diffusive logistic model with radial symmetry is considered. This used in various fields to describe the dynamics of spreading different media: fire propagation, population or biological invasions. Due symmetry, free boundary can be treated by a front-fixing approach resulting fixed-domain non-linear problem, which solved an explicit finite difference method. Qualitative numerical analysis establishes stability, positivity and monotonicity conditions. Special attention paid spreading–vanishing dichotomy algorithm for proposed. Theoretical statements are illustrated tests.