Behavior of first order differential equations through a monte carlo based algorithm

The aim of this study is to show how stochastic approaches can be applied to a deterministic model. Therefore, an algorithm based on the Monte Carlo simulation has been presented for solving some stiff ordinary differential equations and systems of differential equations. Various forms of the differential equations have been solved by using the produced algorithm and compared with the analytical and numerical solutions. The suggested approach has been seen to produce more accurate results than the numerical techniques. To analyze the solution of the system of equations, population models have been taken into consideration. A detailed discussion about the results has also been given to properly realize the behavior of the problems represented by the model equations. Also, the advantages and disadvantages of the method have been exhibited by illustrating both qualitative and quantitative results of the problems of interest.