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In this paper we simulate positive solutions, large solutions and metasolutions of the heterogeneous logistic equation in a diskand an annulus. The numerical methods introduced in this paper areextremely innovative because they make unnecessary determining anyprevious lifting and solving any decoupled system of ordinary differential equations. Moreover, they can be used to solve non-radially symmetric problems. The models are of a huge interest in Spatial Ecologybecause they enable us to analyse the effects of the spatial heterogeneityon the evolution of the terrestrial ecosystems. The large solutions andthe metasolutions have been computed by the first time in this paper.
heterogeneous logistic equation; unequal distribution of resources; spectral methods; collocation methods; numerical simulation of large solutions and metasolutions