A numerical scheme for continuous population models for single and interacting species

Yalçın Öztürk, Ayşe Anapalı, Mustafa Gülsu

Öz


In this article, the dynamic of models such as logistic growth model, prey-predator model and 2-species Lotka-Volterra competition model is approximately solved by the Chebyshev collocation method.  These nonlinear mathematical models are transformed into the matrix form by Chebyshev expansion method and converted nonlinear algebraic equation system. Chebyshev coefficients are obtained by solving nonlinear equation system. Results are compared with Homotopy perturbation and Adomian decomposition method and then comparision numerical result and exact solution are presented by graphics for logistic growth model. Plots are showed the numbers of prey and predator versus time for various N values on predaor prey model. In the 2 spices Lotka Volterra competition model numerical results are presented by graphics. Matlab R2010a and Mapple14 are used for all calculations and graphs. In the conclusion part, the CPU times of the programs are given and the models are compared


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