Abstract
An analytical expression for the solution of the prey-predator problem by an adaptation of the homotopy analysis method (HAM) is presented. The HAM is treated as an algorithm for approximating the solution of the problem in a sequence of time intervals; that is, HAM is converted into a hybrid numeric-analytic method called the multistage HAM (MSHAM). Comparisons between the MSHAM solutions and the fourth-order Runge-Kutta (RK4) numerical solutions reveal that the new technique is a promising tool for the nonlinear systems of ordinary differential equations.
Highlights
Most modelling of biological problems is characterized by systems of ordinary differential equations ODEs
The relationship of increasing and decreasing in the population of two kind of animals such as rabbits and foxes can be described by the socalled mathematical model of the prey-predator problem which is given by a system of nonlinear equations: dx t dt x t a − by t, x t0
Yusufoglu and Erbas 4 and Rafei et al 5 employed the variational iteration method VIM to compute an approximation to the solution of the system of nonlinear differential equations governing the problem
Summary
Most modelling of biological problems is characterized by systems of ordinary differential equations ODEs. Alomari et al introduced a new reliable algorithm based on an adaptation of the standard HAM to solve Chen system In recent years, this method has been successfully employed to solve many types of problems in science and engineering 21–28. We are interested to find the approximate analytic solution of the system of coupled nonlinear ODEs 1.1 by treating the HAM as an algorithm for approximating the solution of the problem in a sequence of time intervals. We shall call this technique as the multistage homotopy analysis method MSHAM. Comparison with the classical fourth-order Runge-Kutta RK4 shall be made
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