An unconditionally stable numerical scheme for competing species undergoing nonlocal dispersion

Abstract

Nonstandard numerical approximation for the study of a competition model for two species that experience nonlocal diffusion, or dispersion, allows for faithful representation of the theoretical solution to the system. Such a scheme may preserve positivity of solutions, be uniquely solvable, and be completely stable. Under appropriate conditions, the error between the scheme and the theoretical solution can be measured. We present such a scheme here and confirm its desirable properties as they reflect the solution to the system.

Keywords

• finite difference scheme
• convergence
• nonstandard scheme
• competition model
• population dynamics