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.
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