Solution of second-order IVP and BVP of matrix differential models using matrix DTM

Abstract

We introduce a matrix form of differential transformation method (DTM) and apply for nonlinear second-order initial value problems (IVPs) and boundary value problems (BVPs) of matrix models which are given by u (t)=f(t,u(t), u ′ (t)) and subject to initial conditions u(a)= u 0, u ′ (a)= u 1 and boundary conditions u(a)= u 0, u(b)= u 1, where u 0, u 1 R r×q. Also the convergence of present method is established. Several illustrative examples are given to demonstrate the effectiveness of the present method. Copyright © 2012 Reza Abazari and Adem Klcman.