An Enhanced Solution of Logistic Model by Applying Differential Transform Method

Abstract

The Differential Transform Method (DTM) is a numerical technique, which results in an analytical solution in the form of polynomials. Although, the method is applied to number of linear and nonlinear boundary and initial value problems, but its generalization needs to be further investigated. This technique is capable of reducing the size and time of computational work in obtaining the exact solutions. The method is used for finding the coefficients for the Taylor’s series. The efficiency and easiness of the method is investigated over the logistic problems. The approximated results are compared with that of exact solutions.  The numerical results obtained through this technique in this research work are found in good agreement to the existing exact solutions which is very clearly presented in the form of tables and graphs. It has been perceived accordingly that the DTM is easier and effective technique to get a series solution in the form of variables, and the results have shown incredible performance of the proposed method. The numerical results and its comparison also show that the proposed method gives realistic results which is more effective for solving logistic problems.