Tetra geoemtric mean Runge-Kutta analysis of bioeconomic fisheries model

The optimal management and utilization of natural resources is eventually important, due to increase in the consumption of natural resources and in view of this, the main aim of fisheries is to maintain the marine organisms at levels that produces maximum sustainable yield (MSY). In this study, the one step numerical approximations schemes are developed to find the solution of such bioeconomic fisheries models whose analytical solution is not possible. In the proposed work, the explicit Runge-Kutta scheme based on fourth order tetra geometric mean is established and this method solve fishery management models of Schaefer and Gordon-Schaefer. The models analyze bioeconomic growth rate, carrying capacity, total and marginal costs and revenues. In solving, the models through proposed tetra geometric mean Runge-Kutta method, it is obtained that the method is easy to implement. The results obtained are much better as compared to other methods when compared in terms of errors and central processing unit (CPU) time.