A NUMERICAL STUDY OF THE SPRUCE BUDWORM REACTION‐DIFFUSION EQUATION WITH HOSTILE BOUNDARIES

ABSTRACT. One of the interesting single species reaction diffusion problems is the spruce budworm model describing insect dispersal behavior. In an earlier study, Singh et al. [7] considered the two‐dimensional spruce budworm model with density dependent diffusion balanced by an artificial wind equal to the population gradient. Here we extend the model by considering more realistic density dependent diffusion and advection with hostile boundaries. We solve this model using a splitting method in which advection, diffusion and reaction processes are separated. Various hostility conditions have been used at the boundary. The numerical results show that the population moves quickly to a steady state outbreak situation when the advective components due to the density dependent diffusion are included.