Solutions of Different Types of the Linear and Non-Linear Higher-Order Boundary Value Problems by Differential Transformation Method

Abstract

In [12], a numerical comparison between the differential transform method and Adomian decomposition method for solving fourth-order boundary value problems was presented. In this article, we use the differential transformation method (DTM) to solve the linear and non-linear higher-order boundary value problems (HOBVPs). The method proved to be very successful and powerful in computing such elements. The specific problems chosen for this purpose is that of the different types of higher order (e.g. fifth, sixth, ninth, tenth and twelfth) boundary value problems. The differential transformation (DT) solutions are compared with the theoretical solution. It is shown that the solutions obtained from the technique have a very high degree of accuracy.