Second Order Runge-Kutta Method in Solving Renewable Natural Resources Model Case Study: Fishes and Water Resources Management

Abstract

This research presents a study of a dynamical system which models natural resources. Using fishes and water resources as the case study. In this work a model equation was used to determine the density of the resources. We also introduced second stage Runge Kutta method, which was used to obtain the result for harvesting terms  from 10% to 50% producing the population of life in the pond after each harvesting. In this research work, the solution of a dynamic system that can model natural resources using the second stage Runge-Kutta method was reported. To actualize this result, a model, a first order ordinary differential equation and the famous Runge-Kutta second stage method is used. Harvesting terms  from 10% to 50% is used for the iteration to demonstrate the validity of the result. The result of this study was applied to the population of fish in a pond, which is a renewable natural resource, with great success. In line with the objectives stated at the beginning of the work, the results of this research has shown that by applying the second order Runge-Kutta method, the solution of a dynamical system can be obtained and applied to model natural resources with great success.