Parameter estimation and numerical solution of predator-prey model using multistep central difference method and block method

Differential equations are vastly adopted for modelling real life scenarios with certain parameters representing selected variables in the model. In cases where real data is utilized, the parameters of the differential equation need to be estimated based on the data, but majority of the techniques adopted in parameter estimation requires that the exact form of the function is known. This is unfortunately not the case when considering differential equations because in many instances the differential equation cannot be solved analytically, hence numerical methods are introduced to obtain an approximate solution. This article describes the development of a multistep central difference method using Taylor series expansion of a generalised multistep central difference scheme to estimate the parameters in the predator-prey model via derivative approximation in application to real data. The results obtained agree with existing study and the numerical solution of the model based on these parameters is obtained using block method. Hence, this article has presented an approach for solving the predator-prey model when considering real data.