A positivity preserving nonstandard finite difference scheme for a systemof reaction diffusion equations with nonlocal initial conditions
A significant number of ecological phenomena can be modeled using nonlinear reaction diffusion partial differential equations. This paper considers a system of reaction diffusion equations with nonlocal initial conditions. Such equations arise as steady state equations in an age structured predator prey model with diffusion. We use the non standard finite difference method developed by Mickens, which is a scheme that preserves the positivity of solutions. Furthermore, this scheme is explicit and functional relationship is obtained between the time, the space, and age step sizes.