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Numerical-analytical solutions of predator-prey models
(World Scientific and Engineering Academy and Society, 2013-01-01) González-Parra Gilberto, G.; Arenas, A.J.; Cogollo, M.R.; Universidad EAFIT. Escuela de Ciencias; Modelado Matemático
This paper deals with the construction of piecewise analytic approximate solutions for nonlinear initial value problems modeled by a system of nonlinear ordinary differential equations. In real world several biological and environmental parameters in the predator-prey model vary in time. Thus, non-autonomous systems are important to be studied. We show the effectiveness of the method for autonomous and non-autonomous predator-prey systems. The method we have used is called the differential transformation method which has some suitable properties such as accuracy, low computational cost, easiness of implementation and simulation as well as preserving properties of the exact theoretical solution of the problem. The accuracy of the method is checked by numerical comparison with fourth-order Runge-Kutta results applied to several predator-prey examples.