The numerical solutions of differential transform method and the Laplace transform method for a system of differential equations

The differential transform method is one of the approximate methods which can be easily applied to many linear and nonlinear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. In this paper, we present the definition and operation of the one-dimensional differential transform and investigate the particular exact solutions of system of ordinary differential equations that usually arise in mathematical biology by a one-dimensional differential transform method. The numerical results of the present method are presented and compared with the exact solutions that are calculated by the Laplace transform method.