A non-linear high order explicit differential transform based method for solving initial value problems

In this paper, a reliable non-linear high order explicit differential transform based method for solving initial value problems of ODEs is presented. The method is based on deriving a general nonlinear relation between the dependent variable and its derivatives from the well known differential transform method. The method results in rational explicit one step integration schemes with arbitrary-order accuracy. The error and stability analysis of the method is presented. Some stiff and non- stiff initial value problems are solved to illustrate the performance and accuracy of the method.