In order to investigate the impact of periodically evolving domain on the mutualism interaction of two species, we study a mutualistic model on a periodically evolving domain. To overcome the difficulty caused by the advection and dilution terms, we transform the model to a reaction–diffusion problem in a fixed domain. By means of eigenvalue problems, the threshold parameters are introduced. The asymptotic profiles of the solutions on an evolving domain are studied by using the threshold parameters and the upper and lower solutions method. The impact of the domain evolution rate on the persistence or extinction of species is analyzed. Numerical simulations are performed to illustrate our analytical results.

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In this article, we present a comparative study between Adomain decomposition method and the new integral transform "Elzaki Transform". We use the methods to solve the linear Partial differential equations with constant coefficients.

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